You are absolutely right. This is a tricky problem in the sense that if you don't realize the technique that you have to use to solve this problem in the beginning, then you're completely screwed.
Here's the technique:
Recall the difference of 2 squares: a^2-b^2=(a-b)(a+b)
Now, we're told to express a in terms of b in the following expression:
a-b=sqrt(a)-sqrt(b)
Apply the difference of two squares on a-b:
(sqrt(a)+sqrt(b))(sqrt(a)-sqrt(b))=sqrt(a)-sqrt(b)
The above expression gives you:
sqrt(a)+sqrt(b)=1
1-sqrt(b)=sqrt(a)
Square both sides of the equation:
1-2sqrt(b)+b=a
C
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Tricky Problem
Source: Beat The GMAT — Problem Solving |
Nice work truplayer... You're right.. the key to solve this problem is to recognize ... (a-b ) is equal to (sqrt a - sqrt b ) ( sqrt a + sqrt b)truplayer256 wrote:You are absolutely right. This is a tricky problem in the sense that if you don't realize the technique that you have to use to solve this problem in the beginning, then you're completely screwed.
Here's the technique:
Recall the difference of 2 squares: a^2-b^2=(a-b)(a+b)
Now, we're told to express a in terms of b in the following expression:
a-b=sqrt(a)-sqrt(b)
Apply the difference of two squares on a-b:
(sqrt(a)+sqrt(b))(sqrt(a)-sqrt(b))=sqrt(a)-sqrt(b)
The above expression gives you:
sqrt(a)+sqrt(b)=1
1-sqrt(b)=sqrt(a)
Square both sides of the equation:
1-2sqrt(b)+b=a
C
Abdulla
