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What is the product of all roots of the equation √x+1 = x-

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What is the product of all roots of the equation √x+1 = x-

by Max@Math Revolution » Thu May 09, 2019 1:34 am

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[GMAT math practice question]

What is the product of all roots of the equation √x+1 = x-√x-1?

A. 1
B. 2
C. 3
D. 4
E. 5
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by Max@Math Revolution » Sun May 12, 2019 5:32 pm
=>

√x+1 = x-√x-1
=> 2√x = x-2
=> 4x = (x-2)^2, after squaring both sides,
=> 4x = x^2-4x+4
=> x^2-8x+4 = 0

If p and q are roots of a quadratic equation, then the quadratic equation is (x-p)(x-q) = 0 or x^2 -(p+q)x + pq = 0.
The constant term pq is the product of the roots.

Thus, the constant term 4 of the equation x^2-8x+4 = 0 is the product of the roots of the equation √x+1 = x-√x-1.

Therefore, the answer is D.
Answer: D
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