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Problem Solving (PS) | If x - 7 = √x + √7 , x = ?

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MathRevolution wrote:

If \(x - 7 = √x + √7\) , x = ?

A. 8 + 2√7
B. 8 - 2√7
C. 8 + √7
D. 8 - √7
E. 7 + 2√8


SandhyAvinash wrote:

please provide in depth explanation of this please

\((x - 7)\) can be written in\((a^2 - b^2) = (a+b)(a-b)\) format. Where;\((x - 7)\) is\((a^2 - b^2)\)

Therefore;\((x - 7) = (√x + √7)(√x - √7)\)

\(x - 7 = √x + √7\)
\((√x + √7)(√x - √7) = √x + √7\)
\( (√x - √7) =\frac{(√x + √7)}{(√x + √7)}\)
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