Sum of a positive single digit number, its square & its cube is 3 more than a perfect square number.

Kushagra Tiwari   9 years AGO

according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a
perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816
it is clear from above that only 1,3,4
gives perfect square
so the sum will be 1+3+4 = 8

Like? Yes (15) | No (3)  

BHASKAR MANDAL   9 years AGO

according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816

it is clear from above that only 1,3,4 gives perfect square
so the sum will be 1+3+4 = 8
option 5 is the answer

Like? Yes (17) | No (6)  

Sourojit Dhua   9 years AGO

The numbers will be: 1,3 and 4
Sum=8

Like? Yes (6) | No (3)  

Dr.Dipin Singh   9 years AGO

such numbers are 1,3,4.
Their sum =8

Like? Yes (2) | No   

Thejas   9 years AGO

1+4+3

Like? Yes (1) | No   

saimeera   9 years AGO

the numbers are 1,3,4
so their sum is 8

Like? Yes (1) | No   

TINKU MITTAL   9 years AGO

answer is 8, here is my explanation
according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816

it is clear from above that only 1,3,4 gives perfect square
so the sum will be 1+3+4 = 8

Like? Yes (1) | No   

Mohan   9 years AGO

1+3+4=8

Like? Yes (1) | No   

CHANDAN KUMAR   9 years AGO

no. will be 1,3,4
sum will be=8

Like? Yes (1) | No   

jasmine kaur   9 years AGO

n2

Like? Yes (1) | No   

soni dabas   9 years AGO

ans. is 8

Like? Yes (1) | No   

AAKANCHA SRIVASTAV   9 years AGO

only 1,3 and 4are such single digits
so there sum is
1+3+4=8

Like? Yes (1) | No   

Anoop Tiwari   9 years AGO

lets check from 1 to 9
1+1^2 + 1^3 -3 = 3-3 = 0
similarily 2+2^2+2^3 -3 = 11,
3+3^2+3 ^3- 3 = 36
4+4^2+4^3- 3 =81
5+5^2+5^3 - 3 =152
6+6^2+6^3 -3 = 255
7+7^2+7^3 - 3 = 396
8+8^2+8^3 -3 = 584
9+9^2+9^3 -3 = 816
we can see that only 1,3,4 are giving perfect square,hence their sum=1+3+4=8

Like? Yes (1) | No   

Aishwarya Chandra   9 years AGO

Frm question
1+1^2 + 1^3 -3 = 3-3 = 0, which is a perfect square
Other chances are
3 + 9 + 27 - 3 = 36
and 4 + 16 + 64 - 3 = 81

(1+3+4) = 8(answer)

Like? Yes (1) | No   

Gitanjali K   9 years AGO

answer is 8

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RAKESH   9 years AGO

x + x^2 + x^3 = y^2 + 3

=> x = 1,3,4
sum =8

Like? Yes (1) | No   

ADARSH GAURAV   9 years AGO

8 is the answer.

Like? Yes (1) | No   

kishore muddada   9 years AGO

let x be the +ve single digit no
so x+x^2+x^3=3+perfect square
x+x^2(1+x)+1=4+perfect square
(1+x)(1+x^2)=4+perfect square
x=1 perfect square=0
x=2 perfect square= NA
x=3 perfect square=36
x=4 perfect square=81
x=5 perfect square=NA
x=6 perfect square=NA
x=7 perfect square=NA
x=8 perfect square=NA
x=9 perfect square=NA
so sum of all such single digit numbers will be 8

Like? Yes (1) | No   

RISHABH SHARMA   9 years AGO

only possbile numbers are 1 ,3 AND 4

Like? Yes (1) | No   

harini   9 years AGO

1+1^2+1^3-3=0
2+2^2+2^3-3=11
3+3^2+3^3-3=36
4+4^2+4^3-3=81
perfect squares for single digit numbers is possible for 1,3,4 only so
sum of 1,3,4 is 1+3+4=8
option 5

Like? Yes (1) | No   

vivek   9 years AGO

only 1+3+4=8 can be possible

Like? Yes (1) | No   

Sreetama Dam   9 years AGO

1+1+1=3 ;3-3=0,perfect square
3+9+27=39;39-3=36,perfect square
4+16+64=84;84-3=81,perfect square
rest 2,5,6,7,8,9 do not fulfill this condition
so result =1+3+4=8

Like? Yes (1) | No   

satyam sharma   9 years AGO

let the number be "x"
x+x^2+x^3=3+perfect square number
in this equation , only 1 and 3 satifies. so sum of these numbers are 4. that is correct answer will be option 8

Like? Yes (1) | No   

viresh pratap singh   9 years AGO

only 1, 3 and 4 satisfy the above relation

Like? Yes (1) | No   

Anusha   9 years AGO

only 1,3,4 are such number...when we add them it becomes 8...so option 5 is correct

Like? Yes (1) | No   

prem kumar   9 years AGO

according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816

it is clear from above that only 1,3,4 gives perfect square
so the sum will be 1+3+4 = 8

Like? Yes (1) | No   

Namrata Gupta   9 years AGO

y is a perfect square no.
x+x2+x3=3+y
the no 1,3,4 satisfy this eqn.
sum of 1+3+4=8

Like? Yes (1) | No   

rakhi kumari   9 years AGO

checking for each digit

Like? Yes (1) | No (1)  

SOURABH   9 years AGO

following are the no.
1,3,4
sum=1+3+4=8

Like? Yes (1) | No (1)  

NAVEEN KUMAR   9 years AGO

x x^2 x^3 (x+x^2+x^3)-3 perfect sqr
0 0 0 -3 no
1 1 1 0 yes
2 4 8 11 no
3 9 27 36 yes
4 16 64 81 yes
5 25 125 152 no
6 36 216 165 no
7 49 343 396 no
8 64 512 581 no
9 81 729 816 no
hence,
Sum of all such single digit numbers will be(all 'yes')=1+3+4=8
option(5)

Like? Yes (2) | No (2)  

abhinav singh   9 years AGO

(a+a^2+a^3-3)=perfect square
this condition satisfies 1, 3, 4
sum of these no.=1+3+4
=8
option is 5

Like? Yes (2) | No (2)  

santosh kumar patel   9 years AGO

sqrt(a+a^2+a^3-3)=a(perfect)........ natural number
hence 1,3,4 are the numbers
so Sum of the numbers=1+3+4=8

Like? Yes (2) | No (2)  

sanjeev kumar   9 years AGO

ans is 1+3+4=8

Like? Yes (1) | No (1)  

Chandra chur anand   9 years AGO

as per by Q
x+x^2+x^3=x^2+3
or sqrt(x+x2+x^3-3=x)
so for 1 it ll give 0
for 3 it ll give sqrt(36)
and for 4 it ll give sqrt(81)
so 1+3+4=8 ans..

Like? Yes (1) | No (1)  

Deepu Kumar   9 years AGO

sqrt(a+a^2+a^3-3)=a natural number
1,3,4 are the numbers
so Sum of the numbers=1+3+4=8
SO OPTION 5 IS CORRECT.

Like? Yes (1) | No (1)  

Akshay   9 years AGO

1,3,4 are single digit numbers for which these no. itself ,its square and cube is 3 more than perfect square ;
hence their sum is 8.

Like? Yes (1) | No (1)  

niraj   9 years AGO

1+3+4=8

Like? Yes (1) | No (1)  

Gaurav Sharan   9 years AGO

1+1*1+1*1*1=0+3
3+9+27=39=36+3
4+16+64= 84= 81+3
so, 1+3+4=8

Like? Yes (1) | No (1)  

SAI KIRAN   9 years AGO

verified whether (x+x^2+x^3)-3 is perfect square, where x is a single digit positive number.

Like? Yes (1) | No (1)  

himanshu jaiswal   9 years AGO

only 1,3,4 satisfy the given condition
so the ans will be their sum = 8

Like? Yes (1) | No (1)  

stuti priyambda   9 years AGO

1+3+4=8

Like? Yes (1) | No (1)  

satyam shivam   9 years AGO

according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816

it is clear from above that only 1,3,4 gives perfect square
so the sum will be 1+3+4 = 8

Like? Yes (1) | No (1)  

Chirag Ranjan Lahiri   9 years AGO

From the question, we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a perfect square
Similarly the other possibilities are
3 + 9 + 27 - 3 = 36
and 4 + 16 + 64 - 3 = 81

Hence the answer will be : (1+3+4) = 8(answer)

Like? Yes (1) | No (1)  

Sanchit Kapoor   9 years AGO

Such digits are 1,3 and 4 as
1+1+1=3=(0)^2+3
3+9+27=39=(6)^2+3
4+16+64=84=(9)^2+3
So their sum=1+3+4=8
Thus option 5 is correct

Like? Yes (2) | No (3)  

pawan kumar   9 years AGO

1+3+4=8

Like? Yes (1) | No (2)  

pritika singh   9 years AGO

only 3 nos. satisfy cndition
1+1^2+1^3=3= (0+3) 0 prfct sqr
3+3^2+3^3=39=(36+3) 36 prfct sqr
4+4^2+4^3=84=(81+3) 81 prfct sqr
hence, 1+3+4=8

Like? Yes (2) | No (3)  

NAGENDRA P   9 years AGO

1+4+3=8

Like? Yes (1) | No (2)  

ABHILESH PURI GOSWAMI   9 years AGO

solve taking all one digit no.

Like? Yes (1) | No (2)  

Jagruti   9 years AGO

answer = 8
there r only 3 such single digit numbers,viz.,1.,3.,4
1+1^2+1^3-3=0....a perfect square
3+3^2+3^3-3=36....a perfect square
4+4^2+4^4-3=81...a perfect square
1+3+4=8
so ans = 8

Like? Yes (1) | No (2)  

swarupa nuggu   9 years AGO

8

Like? Yes (1) | No (2)  

DEEPAK GOSWAMI   9 years AGO

1 3 4 only 3 num r there nd d sum of these r 8

Like? Yes (1) | No (2)  

S.SHAFI   9 years AGO

a + a^2 + a^3 = 3 + (perfect square number);
1 + 1+ 1 = 3 +(0) ;
3 + 9 + 27 = 3 + (36);
4 + 16 + 64 = 3 + (81);
it will work for only 1, 3, 4....
rest of them it won't satisfy the equation...
so sum of digits is 8...

Like? Yes (1) | No (2)  

Shreya Tiwari   9 years AGO

according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a
perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816
it is clear from above that only 1,3,4
gives perfect square
so the sum will be 1+3+4 = 8

Like? Yes (1) | No (2)  

Supriya_kamkar   9 years AGO

1+1^2+1^3=0+3

3+3^2+3^3=36+3

4+4^2+4^3=81+3

there are no other such numbers.

1+3+4=8

Like? Yes (1) | No (2)  

Abhishek Vishwakarma   9 years AGO

according to question we can write
1+1^2 + 1^3 -3 = 3-3 = 0, which is a
perfect square
2+4+8 -3 = 11,
3+9+27 - 3 = 36
4+16+64- 3 =81
5+25+125 - 3 =152
6+36+216 -3 = 255
7+49+343 - 3 = 396
8+64+512 -3 = 584
9+81+729 -3 = 816
it is clear from above that only 1,3,4
gives perfect square
so the sum will be 1+3+4 = 8

Like? Yes (1) | No (2)  

lakshmi nalluri   9 years AGO

only 1,3,4 are applicable for above condition
sum=1+3+4=8
given ,
x+x^2+x^3=3+A^2
possibilities of x =[1,9]
only,1,3,4 are applicable

Like? Yes (1) | No (2)  

Kethineni Vinodh   9 years AGO

1,3,4
then sum is 8

Like? Yes (1) | No (2)  

Devendra Marghade   9 years AGO

1+1^2+1^3=3 =0+3
3+3^2+3^3=39=36+3
4+4^2+4^3=84=81+3
So sum of such single digit numbers=1+3+4=8

Like? Yes (1) | No (2)  

Nirmal Kumar Thakur   9 years AGO

1+1*1+1*1*1=1=0+3
3+3*3+3*3*3=39=6*6+3
4+4*4+4*4*4=84=9*9+3

Like? Yes (1) | No (2)