Question
When x is added to each of 9, 15, 21 and 31, the numbers
so obtained are in proportion. What is the mean proportional between the numbers (3x-2) and (5x+4)?Solution
According to Question- (9 + x)/(15 + x) = (21 + x)/(31 + x) ⇒ (9 + x)(31 + x) = (15 + x)(21 + x) ⇒ x2 + 40x + 279 = x2 + 36x + 315 ⇒ 4x = 36 ⇒ x = 9 Mean proportion of (3x - 2) and (5x + 4) = √{(3×9 - 2)(5×9 + 4)} ⇒ √(25 × 49) ⇒ 35
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