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(#M40156010) ELITMUS Numerical Ability question Keep an EYE

how many solutions to this equation:
sqrt(x+7)=x*sqrt(x+7)

Asked In Elitmus insha singh (9 years ago)

Unsolved Read Solution (18)

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Read Solution (18) :

Rupesh Chouksey  (9 years ago)

Ans is 3
sqrt(x+7)=x*sqrt(x=7)
by squaring both sides
x+7=x^2(x+7)
x^3+7x^2-x-7=0
which has three roots -1,1,-7

Is this solution Helpfull? Yes (16) | No (10)  

garima nayak  (9 years ago)

sorry its 2
sqrt(x+7)=x*sqrt(x+7)
on cancelling sqrt(x+7) i.e. x=1
and sqrt(x+7) can be 0 also, therefore x+7=0 hence x=-7
therefore x=1,x=-7

Is this solution Helpfull? Yes (14) | No (7)  

satyajeet das  (9 years ago)

@richa
putting -1 in the initial equation it does not satisfy so -1 is not a solution.

Is this solution Helpfull? Yes (10) | No   

abhishek chaubey  (9 years ago)

in mathematics...its always suggested to not to change the degree of an equation since it may results in unnecessary roots termed as EXTRANEOUS ROOTS"...fr example if we have an simple equation say x=5 then it has only one root ie 5 (most obvious) ...however if we make square of both sides then it will be like x^2=25 and now it will have two roots x=+5 and x=-5 which is infact not appropriate with the basic equation x=5......so the buddies here who have answered it as 3 roots is not correct...it will have only 2 roots...-7 and 1

Is this solution Helpfull? Yes (8) | No   

richa gargi  (9 years ago)

sqrt(x+7)=x*sqrt(x+7)
squaring both sides
(x+7)=x^2 (x+7)
not takin x+7 to other side
x^2 (x+7)-(x+7)=0
now takin x+7 common
(x+7)(x^2 -1)=0
this means
either x+7=0
or
x^2 -1=0
or both
so if x+7=0
x=-7
if x^2-1=0
x^2=1
x=+1 or -1
so x has three soln
x=1,-1,-7

Is this solution Helpfull? Yes (7) | No (5)  

Subha Mahapatra  (9 years ago)

ANS : 2

if we simplify the the equation, we will get :
(x+7) = x^2 * (x+7)
or, x^2 = 1
so, X = 1 and -1.

The number of solution is 2

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

Aditi  (9 years ago)

Since solution is unique the no.of solution should be 1 but the no.of roots is 3

Is this solution Helpfull? Yes (3) | No (1)  

jitendra kumar singh  (9 years ago)

ans is 2
sqrt(x+7)=x*sqrt(x+7) ..................equ..1
by squaring both side
x+7=x^2(x+7)
x^2(x+7)-(x+7)=0
take common x+7
(x+7)(x^2-1)=0
(x+7)(x-1)(x+1)=0
so we get
x=7,x=1,x=-1
this value put in equation (1)
x=-1 not satisfying the equation
hence only two solution of this equation.

Is this solution Helpfull? Yes (3) | No (1)  

garima nayak  (9 years ago)

i think its 1

Is this solution Helpfull? Yes (1) | No (3)  

mohit  (9 years ago)

after getting roots we should satisfy them in original equation as roots were obtained by modifying the equation. hence only 1,-7 are valid answers , -1 is NOT.

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

L.Susmi  (8 years ago)

i think it has only 1 solution for any value of x sqrts get cancel finally in the equation we get x=1 so only i solution
rectify me if iam wrong

Is this solution Helpfull? Yes (1) | No   

Vishal Upadhyay  (6 years ago)

Its Always 1 Because here only one Variable ie.X So May be x have different different Value but Solution is only 1.

Is this solution Helpfull? Yes (1) | No   

insha singh  (9 years ago)

how? @garima

Is this solution Helpfull? Yes | No (1)  

vikash  (9 years ago)

1, x=1, x=sqrt(x+7)/sqrt(x+7)

Is this solution Helpfull? Yes | No (1)  

Himanshi  (8 years ago)

since the above equation is a quadratic equation so the number of solutions will be three.

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shehzad  (8 years ago)

there are only two solutions x= 1 and x= -7 since x=-1 doesnt satisfy the original equation

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abhishek upadhyay  (8 years ago)

3....This equation will be in power of 3

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lakhan jain  (5 years ago)

The degrees should never be altered in such type of questions because you land up with n number of solutions because you can alter/keep increasing the degree of equation n times.So
The highest degree in the equation is 1 therefore only one solution possible.

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