Question
If 3, x, y, 48 are in GP and x, y, 45 in AP, find x and
y.Solution
ATQ,
GP: x²=3y, y²=48x. AP: 2y = x + 45. From first: y= x²/3. Substitute → 2(x²/3) = x + 45 → 2x² = 3x + 135 → 2x²–3x–135=0. x= (3 ± √(9 + 1080))/4 = (3 ± 33)/4 → x=9 or –7.5. Take positive → x=9 → y=27. ✔ x = 9, y = 27.
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