Latest TCS Aptitude Question SOLUTION: In this question, X^Y means, X raised to the power Y. How many integers x satisfy the equation (x^2 - x - 1)^(x + 2)= 1? o 4 o 2 o 3 o None of the other 3 choices

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In this question, X^Y means, X raised to the power Y. How many integers x satisfy the equation (x^2 - x - 1)^(x + 2)= 1?
o 4
o 2
o 3
o None of the other 3 choices

Asked In TCS Nakshatra Mukhopadhyay (8 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Puja Dhar  (8 years ago)

answer is 4
because from(x^2-x-1) you'll get 2
values of x.
and power should be 0 to get the 1
x+2=0
x=-2
and if you put x=1
then also you'll get 1 in rhs
sono of total values of x is 4

Is this solution Helpfull? Yes (12) | No (7)  

Satwik  (8 years ago)

answer is 4 solutions ,x=-1,-2,0,2

Is this solution Helpfull? Yes (8) | No (1)  

vidya bharati  (8 years ago)

It should be 3 because only 0,-1 and 2 are satisfying this equation.

Is this solution Helpfull? Yes (3) | No (4)  

Achal Rai Kanungo  (8 years ago)

4 integer values will satisfy this equation
for (x^2-x-1)^(x + 2)=1 there are certain cases :
1. on equating both equations (x^2 - x - 1)^(x + 2)=1^1 then x+2=1 &x=-1
2. value of (x^2-x-1) can be 1 or -1, (x^2-x-1)=1 equation will have real roots
(x^2-x-1)=-1 will give x=0 & x=1, out of which x=0 will satisfy equation
3. from 2nd case if (x^2-x-1)=-1 then x+2 can hold only even values i,e. 2,4,6,8....
that will give x=0,2,4... but only x=0 & x=2 will satisfy the equation
4. value of x+2 can be 0 i.e, x+2=0,x=-2
so 4 integer values -2,-1,0,2 will satisfy the equation

Is this solution Helpfull? Yes (2) | No   

Ashalekshmi K G  (8 years ago)

Taking log on both sides.
>> (x+2).log(x^2-x-1)= log 1 =0.
>>either (x+2) =0 or log(x^2-x-1)=0.
x+2=0 >> x=-2.
log(x^2-x-1)=0 >> (x^2-x-1)=e^0 = 1
>> x^2-x-2=0
>> x=5, -4.
So the answer is 3, and the solutions are -2, -4, 5.

Is this solution Helpfull? Yes (1) | No (2)  

Vanaja  (8 years ago)

4
((-2)^2)-2-1)^(-2+2)=1
((0)^2)-0-1)^(0+2)=1
((2)^2)-2-1)^(2+2)=1
((-1)^2)-(-1)-1)^(-1+2)=1

Is this solution Helpfull? Yes (1) | No (1)  

sravanthi kolli  (8 years ago)

only -2,-1,0,2 satisfies hence answer is 4

Is this solution Helpfull? Yes (1) | No   

Yashasvi Pandey  (8 years ago)

FIRST TAKE LOG BOTH THE SIDE IT WILL MAKE
(x+2)log(x^2-x-1)=log1
x+2=log1 log1= 0 x= -2
then x^2-x-1=1
x=,1,2

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RAKESH KUMAR YADAV  (8 years ago)

(x^2-x-1)^(x+2)=1^0
or,x+2=0
or, x=-2
x^2-x-1=1
x=2,-1
no of integers x satisfy=3

Is this solution Helpfull? Yes | No (1)  

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