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Find the value of p which satisfies the equation \(\sqrt P-\frac 6 p = 1\)


Question

Find the value of p which satisfies the equation \(\sqrt P-\frac 6 p = 1\)

Options

A) 4

B) -4

C) 9

D) -9

The correct answer is C.

Explanation:

\(\sqrt P-\frac 6{\sqrt p}=1\)
Multiply through by \(\sqrt P\)
\(P - 6 = \sqrt P\)
Square both side \((P - 6)^{2} = (\sqrt P)^{2}\)
\(P^{2} - 12P + 36 = P\)
\(P^{2} - 12P - P + 36 = 0\)
\(P = 9\) or \(4\)
Check to see if 9 or 4 satisfied the equation
\(\sqrt P-\frac 6{\sqrt P}=1\)
When \(P = 9\)
\(\sqrt 9-\frac 6{\sqrt P}=1\)
\(3-\frac 6 3=1\)
\(3 - 2 = 1\)
\(1 = 1\)
Hence the value p = 9 satisfied the equation when p = 4
\(\sqrt 4-\frac 6{\sqrt 4}=1\)
\(2-\frac 6 2=1\)
\(2 - 3 = 1\)
\(-1 \neq 1\)
Hence the value p = 4 does not satisfy the equation \({\therefore} p = 9\)

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Dicussion (1)

  • \(\sqrt P-\frac 6{\sqrt p}=1\)
    Multiply through by \(\sqrt P\)
    \(P - 6 = \sqrt P\)
    Square both side \((P - 6)^{2} = (\sqrt P)^{2}\)
    \(P^{2} - 12P + 36 = P\)
    \(P^{2} - 12P - P + 36 = 0\)
    \(P = 9\) or \(4\)
    Check to see if 9 or 4 satisfied the equation
    \(\sqrt P-\frac 6{\sqrt P}=1\)
    When \(P = 9\)
    \(\sqrt 9-\frac 6{\sqrt P}=1\)
    \(3-\frac 6 3=1\)
    \(3 - 2 = 1\)
    \(1 = 1\)
    Hence the value p = 9 satisfied the equation when p = 4
    \(\sqrt 4-\frac 6{\sqrt 4}=1\)
    \(2-\frac 6 2=1\)
    \(2 - 3 = 1\)
    \(-1 \neq 1\)
    Hence the value p = 4 does not satisfy the equation \({\therefore} p = 9\)

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