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655-705 (Hard)|   Algebra|      
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Bunuel
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If (x^2 + 4)^(1/2) = x + h, what is the value of x? 03 Apr 2018, 21:39
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D
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Difficulty:

55% (hard)

Question Stats:

60% (01:41) correct 40% (01:18) wrong based on 66 sessions

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

(1) h = 2
(2) h^2 = 4
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D
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kunalcvrce
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If (x^2 + 4)^(1/2) = x + h, what is the value of x? 03 Apr 2018, 23:51
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Bunuel
If \(\sqrt{x^2 + 4} = x + h\), what is the value of x?

(1) h = 2
(2) h^2 = 4
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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
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If (x^2 + 4)^(1/2) = x + h, what is the value of x? Updated on: 04 Apr 2018, 02:00
Originally posted by nishore1 on 04 Apr 2018, 00:21.
Last edited by nishore1 on 04 Apr 2018, 02:00, edited 2 times in total.
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Bunuel
If \(\sqrt{x^2 + 4} = x + h\), what is the value of x?

(1) h = 2
(2) h^2 = 4
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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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If (x^2 + 4)^(1/2) = x + h, what is the value of x? 04 Apr 2018, 00:22
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Bunuel
If \(\sqrt{x^2 + 4} = x + h\), what is the value of x?

(1) h = 2
(2) h^2 = 4
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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
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If (x^2 + 4)^(1/2) = x + h, what is the value of x? 05 Apr 2018, 09:06
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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.
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If (x^2 + 4)^(1/2) = x + h, what is the value of x? 05 Apr 2018, 23:58
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Bunuel
If \(\sqrt{x^2 + 4} = x + h\), what is the value of x?

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

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
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