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\(\sqrt{x}\) - \(\frac{6}{\sqrt{x}}\) = 1, find the value of x

Further Mathematics
WAEC 2024

\(\sqrt{x}\) - \(\frac{6}{\sqrt{x}}\) = 1, find the value of x

  • A. 36
  • B. 16
  • C. 9
  • D. 25
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Correct Answer: Option C
Explanation

\(\sqrt{x}\) - \(\frac{6}{\sqrt{x}}\) = 1

Multiply through by \(\sqrt{x}\)

x - 6 = \(\sqrt{x}\)

x - \(\sqrt{x}\) = 6

let \(\sqrt{x}\) = q, then x = q\(^2\)

q\(^2\) - q - 6 = 0

q\(^2\) - 3q + 2q - 6 = 0

q(q - 3) + 2(q - 3) = 0

(q - 3)(q + 2) = 0

q = 3 or -2

but x =  q\(^2\), meaning, x = 9 or 4.

 


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