Latest Elitmus Aptitude Question SOLUTION: How many solution exist for sqrt(x+7) = x*sqrt(x+7)

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How many solution exist for
sqrt(x+7) = x*sqrt(x+7)

Asked In Elitmus Swati (9 years ago)

Unsolved Read Solution (11)

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Read Solution (11) :

veer kumar  (9 years ago)

there will be 2 solution
sqrt(x+7)=x*sqrt(x+7)=>x=1
sqrt(x+7)-x*sqrt(x+7)=0
sqrt(x+7)(1-x)=0 => x=-7 or 1
squaring both sides
x+7=x^2*(x+7)=>x^2=1 =>x=+-1
thus the values of x are +1,-1,-7
but if we put -1 the original equation we will get imaginary numbers which cant be compared thus we can say that there will be only 2 solution i.e x=1,-7
FRIENDS DON'T JUDGE THE NUMBER OF SOLUTION FROM THE HIGHEST POWER OF 'X' BECOZ WE MAY GET TWO SAME VALUES EXAMPLE: (X-1)^3 HERE WE WILL GET ONLY ONE SOLUTION I.E X=1 BUT POWER OF X IS 3. SO I RECOMMEND U TO SOLVE THE EQUATION

Is this solution Helpfull? Yes (32) | No (1)  

mohit  (9 years ago)

there are 3 solutions as max degee of x is 3 in the eqation

Is this solution Helpfull? Yes (7) | No (11)  

kumar saurav  (9 years ago)

squaring both side we get
(x+7)=x^2*(x+7)
(x+7){1-x^2}=0
then x=+1,-1,-7
three solution exits.

Is this solution Helpfull? Yes (4) | No (8)  

Pramod  (9 years ago)

sqring both side
we have
(x+7)=x^2*(x+7)
here we can cancelleout (x+7) from both sides
when (x+7)is not equals to 0
hence X=-7 will not accepted.
also x^2=0
gives x=-1,+1
butx=-1
not satisfies the original equation
hence only one solution is posible i.e +1.

Is this solution Helpfull? Yes (3) | No (12)  

Kiran kumar raju.G  (9 years ago)

only 2 solutions i.e 1 and -7.
By substituting 1 and -7 only, the above equation can be satisfied.

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

AJEET  (9 years ago)

sqaure from both side
x+7=x^2(x+7)
x=1,-1,7
but original equation satisfied by 1 and 7 so only two solution possible

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Pramod  (9 years ago)

sorry guys in above solution x^2=1 not=0

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Abhishek  (8 years ago)

by putting x=-1 i don't think we would get a imaginary value .then what we would get?
we would get a irrational number not a imaginary number. Although -1 will not satisfy the above equation as sqrt(6) cant be equal to -sqrt(6) {- implies minus} so there is only 2 solution 1,-7 . :)

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sunil awasthi  (9 years ago)

The sol will be two 1 and -7 n can be solved by taking x+7 k2

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sonam  (9 years ago)

only 1 solution that is at x=1

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Navpreet Singh  (9 years ago)

x*sqrt(x+7)-sqrt(x+7)=0
sqrt(x+7)(x-1)=0
x=1 or x=-7

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