What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)?
If x is added to each of numbers, the numbers so obtained in this order are in proportion
so, $$\frac{10 + x}{16 + x} = \frac{22 + x}{32 + x}$$
(10 + x)(32 + x) =Â (16 + x)(22 + x)
320 + 10x + 32x + $$x^2 = 352 + 16x + 22x + x^2$$
320 + 42x = 352 + 38xÂ
4x = 32
x = 8
(x + 1) = 8 + 1 = 9
(3x + 1) = 24 + 1 = 25
Mean proportional = $$\sqrt{9 \times 25}$$ = 15
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