alleryIf the sum of two positive numbers is 6 times their geometric mean, the numbers are in the ratio:
A$(3+2\sqrt2):(3-2\sqrt2)$
B$(2+\sqrt3):(2-\sqrt3)$
C$2:1$
D$3:1$
Answer & Solution
Correct answer: A. $(3+2\sqrt2):(3-2\sqrt2)$
If a+b = 6√(ab), then (a+b)² = 36ab
⟹ a/b solves the resulting quadratic, giving a:b = (3+2√2):(3−2√2).
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