Solve the equation: \(y - 11\sqrt{y} + 24 = 0\)
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Correct Answer: Option B
Explanation:
\(y - 11\sqrt{y} + 24 = 0 \implies y + 24 = 11\sqrt{y}\)
Squaring both sides,
\(y^{2} + 48y + 576 = 121y\)
\(y^{2} + 48y - 121y + 576 = 0 \implies y^{2} - 73y + 576 = 0\)
\(y^{2} - 64y - 9y + 576 = 0\)
\(y(y - 64) - 9(y - 64) = 0\)
\((y - 9)(y - 64) = 0\)
\(\therefore \text{y = 64 or y = 9}\)
\(y - 11\sqrt{y} + 24 = 0 \implies y + 24 = 11\sqrt{y}\)
Squaring both sides,
\(y^{2} + 48y + 576 = 121y\)
\(y^{2} + 48y - 121y + 576 = 0 \implies y^{2} - 73y + 576 = 0\)
\(y^{2} - 64y - 9y + 576 = 0\)
\(y(y - 64) - 9(y - 64) = 0\)
\((y - 9)(y - 64) = 0\)
\(\therefore \text{y = 64 or y = 9}\)