Question 64
If 2x + 1, x + 2, 2 and 5 are in proportion, then what is the mean proportional between 3.5(1 - x) and 8(1 + x)?
Solution
2x + 1, x + 2, 2 and 5 are in proportion. So,
$$\frac{2x + 1}{x + 2} = \frac{2}{5}$$
(2x + 1) $$\times 5 = (x + 2) \times 2 $$
$$10x + 5 = 2x + 4$$
8x = -1
x = -1/8
Mean proportional between 3.5(1 - x) and 8(1 + x)
Numbers = 3.5(1 + 1/8) and 8(1 -1/8) = 31.5/8 and 7
Mean proportional = $$\sqrt{(\frac{31.5}{8} \times 7)}$$ = $$\sqrt{27.5625}$$ = 5.25
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