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Question:

 If x + 2y = 10 and 2xy = 9, then one of the value of x − 2y is:

Explanation:

 Given x + 2y = 10 ⇒ x = 10 - 2y

Also, 2xy = 9, [substituting x = 10 - 2y]

⇒ 2(10 - 2y)y = 9

⇒ 4y² - 20y + 9 = 0

⇒ 4y² - 18y - 2y + 9 = 0

⇒ (2y - 1)(2y + 9) = 0

⇒ y = -9/2 or 1/2

⇒  x = 28 or 9

∴ x - 2y = 28 - (-9) or 9 - (1)
⇒ x - 2y = 37 or 8

Hence, option (d).