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Solve the equation: (y – 11sqrt{y} + 24 = 0)

Solve the equation: (y – 11sqrt{y} + 24 = 0)

  • A.
    8, 3
  • B.
    64, 9
  • C.
    6, 4
  • D.
    9, -8
Correct Answer: Option B
Explanation

(y – 11sqrt{y} + 24 = 0 implies y + 24 = 11sqrt{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})