If x 0, what is the value of x? (1) x is equal to half of its square

Question

If x > 0, what is the value of x?

(1) x is equal to half of its square root
(2) 4x^2 + 7x – 2 = 0

sri46 · Answer

1. 
 x=√x/2 
 2x= √x
 ‎4x^2= x
 ‎4x^2-x=0
 ‎x(4x-1)=0 
 ‎Either x=0 / x=1/4
 ‎since x>0 , therefore x=0.25 
Sufficient 
2.
4x^2+7x-2=0 
Roots = {-7+-(√49+32)}/8 
Roots are 0.25 and -2
Since x>0 therefore x= 0.25 
Sufficient

Imo: D

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yashikaaggarwal · Answer

IMO is D
Statement 1: X=√x/2
Squaring both sides. And then equating,
We get X=1/4>0
(Sufficient)

Statement 2:
4x^2+7x-2=0
4x^2+8x-x-2=0
4x(x+2)-1(x+2)=0
(X+2)(4x-1)=0
X=1/4 & -2
Since X>0
X=1/4 (sufficient)

IMO should be D

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TestPrepUnlimited · Answer

Statement 1:

x = \frac{1}{2}*\sqrt{x} 
 2x =\sqrt{x} 
 4x^2 = x

This is a quadratic equation with one positive solution and x = 0 as another possible solution, however we know x cannot be 0 so we can only accept the positive solution. Sufficient.

Statement 2:

Divide by 4 to write the equation in the standardized form. Observe that the last term is  \frac{-2}{4} , this term is equal to the product of the two solutions for a quadratic equation. We can tell this equation has a positive solution and a negative solution from this  \frac{-2}{4} . Then we can only accept the positive solution of this equation, as x must be positive. So this is sufficient.

Ans: D

AnirudhaS · Answer

(1) x=0 or 1/4
But x>0, so x=1/4
Sufficient

(2) x=-2, or 1/4
But x>0, so x=1/4
Sufficient

Answer:  D

NitishJain · Answer

D?

A: x = sqrt(x)/2. ==> 2x = sqrt(x) ; squaring both sides==> 4x^2 = x; solving this give unique value for x= 1/4 as x> 0

b: 4x^2 + 7x – 2 = 0 ==> solving this give x=4 as x>0

If x > 0, what is the value of x? (1) x is equal to half of its square

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