Latest Elitmus Aptitude Question SOLUTION: How many solutions exists for √(x+5) = x√(x+5) a.1 b.2 c.3 d.4

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How many solutions exists for √(x+5) = x√(x+5)

a.1

b.2

c.3

d.4

Asked In Elitmus Liti (9 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

RAKESH  (9 years ago)

b. 2

√(x+5) = x√(x+5)
=> √(x+5) - x√(x+5) = 0
=> √(x+5)*(1-x) = 0
=> (x+5) = 0 or (1-x)= 0
=> x = 1, -5

if squaring is done then u will get three roots x = -1, 1, -5
but x= -1, doesn't satisfy the given eqn
so, two soln esist.

Is this solution Helpfull? Yes (48) | No (3)  

Prateek Pandey  (9 years ago)

c.3

√(x+5) = x√(x+5)
on squaring both sides we will get
(x+5)=x^2(x+5)
on rearranging the eqution,we will get
=>x^2(x+5)-(x+5)=0

=>(x+5)(x^2-1)=0

=>either (x+5)=0 or (x^2-1)=0

=>hence,x can be -5,1,-1
so there will be three solutions

Is this solution Helpfull? Yes (12) | No (11)  

mohit tuteja  (9 years ago)

ans is 2...
√(x+5)-x√(x+5)=0
take √(x+5) common n there will be two sol for x

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

Anandita Rani  (7 years ago)

Given, sqrt(x+5) = x sqrt(x+5)
Squaring both sides we get:

(x + 5) = x^2(x + 5)

=> x^2(x + 5) - (x + 5) = 0

=> (x^2 - 1)(x + 5) = 0

=> x = 1, -1, -5

so When x = 1:
sqrt(x+5) = x sqrt(x+5)

=> sqrt(1+5) = 1 xx sqrt(1+5)

=> sqrt(6) = sqrt(6) (which is true)

When x = -5:
sqrt(x+5) = x sqrt(x+5)

=> sqrt(-5+5) = -5 xx sqrt(-5+5)

=> sqrt(0) = -5 * sqrt(0)

=> 0 = 0 (which is true)

When x = -1:
sqrt(x+5) = x sqrt(x+5)

=> sqrt(-1+5) = -1 xx sqrt(-1+5)

=> sqrt(4) = -sqrt(4)

=> 2 = -2 (which is not true)

So for the given equation we can have two values of x.

Is this solution Helpfull? Yes (2) | No   

LOKESH RANJAN  (9 years ago)

2,(x+5)=x^2(x+5)=>x^2=1

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Pijush Kar  (9 years ago)

c.3
Nobody said x can't be 0
The solutions are x = 0,1,-5

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vivek keshari  (9 years ago)

no of soutions will be 2

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Natasha Arora  (9 years ago)

There are three solutions but 2 satisfies the condition hence ans is 2

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Amit Bansal  (8 years ago)

c.3

√(x+5) = x√(x+5)
on squaring both sides we will get
(x+5)=x^2(x+5)
on rearranging the eqution,we will get
=>x^2(x+5)-(x+5)=0

=>(x+5)(x^2-1)=0
=>(x+5)(x-1)(x+1)=0
=> 3 solutions

Is this solution Helpfull? Yes | No (2)  

MANIAKANDAN  (8 years ago)

4 sol:arrange as per data.i get 4

Is this solution Helpfull? Yes | No (2)  

shashank kumar  (8 years ago)

ans is 2
on squaring both side we get
x+5 = x^2(x+5)
=> x^2 = 1
=> x =+-1

Is this solution Helpfull? Yes | No (2)  

Raghvendra Singh Patel  (8 years ago)

ans b
√(x+5) = x√(x+5)

take square both side
then
(x+5)=x^2(x+5)
solve it we find
x^2=1
then
x=1,x=-1
we put the value of x in the equation
and satisfy these value
and there are solution

Is this solution Helpfull? Yes | No (1)  

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