If (x^2 + 4)^(1/2) = x + h, what is the value of x?

Question

If  \sqrt{x^2 + 4} = x + h , what is the value of x?

(1) h = 2
(2) h^2 = 4

kunalcvrce · Answer

From1: 
h=2
 \sqrt{x^2 + 4} = x + 2 
squaring both sides: x^2 + 4= (x + 2)^2 
solving this we get x=0

sufficient.

From2:
h=2,-2
 \sqrt{x^2 + 4} = x + 2  &  \sqrt{x^2 + 4} = x - 2

solving both we will get x=0

so sufficient

hence D

nishore1 · Answer

x+2=x+h

h=2 and x =0

Stmnt 1:

x+2 = x+2

True

Stmnt 2:

h^2 = 4
h = + or - 2
 
False

Ans : A

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Hatakekakashi · Answer

1) h=2

we can find a unique value
sufficient

2) h^2 = 4

h= 2 or -2

2 values of x

insufficient

(A)imo

US09 · Answer

IMO D

The equation on simplifying becomes- h(2x+h) = 4.

1) h=2, substituting in our simplified equation we get x=0. Therefore, sufficient.

2) h=+/-2, substituting both values of h in our simplified equation we get x=0. Therefore sufficient.

Hence, D.

amanvermagmat · Answer

A quick look at both statements tells us that we will have to deal with h=2 and h=-2. so we should input both these values in the question stem and check whether it satisfies or not. If we square both sides in question stem, we get: (x^2 + 4) = (x^2 + h^2 + 2xh). Or 4 = h^2 + 2xh

Lets put h=2, we get: 4 = 4 + 4x or 4x = 0 or x=0

Lets put h=-2, we get: 4 = 4 - 4x or -4x=0 or x=0.

In any case, it gives us the same value of x, which is 0. So either statement alone is sufficient. hence  D answer

If (x^2 + 4)^(1/2) = x + h, what is the value of x?

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