Question

Find x,if 16[(a-x)/(a+x)]^3 =(a+x)/(a-x)

Answer 1

$16 (\frac{a - x}{a + x} ) {}^{3} = \frac{a + x}{a - x} \\ ( \frac{a - x}{a + x} ) {}^{4} = \frac{1}{16} \\ \frac{a - x}{a + x} = + - \frac{1}{2} \\ 2a - 2x = a + x \\ x = \frac{a}{3} \\ 2a - 2x = - (a + x) \\ x = 3a$

Answer 2

The value of x is a/3

Solution:

Given that,

$16 (\frac{a - x}{a + x} ) {}^{3} = \frac{a + x}{a - x}$

We have to find the value of x

From given,

$16 (\frac{a - x}{a + x} ) {}^{3} = \frac{a + x}{a - x}\\\\(\frac{a - x}{a + x} ) {}^{3} \times \frac{a-x}{a+x} = \frac{1}{16}\\\\\frac{(a-x)^4}{(a+4)^4} = \frac{1}{16}\\\\Make\ the\ powers\ same\\\\\\frac{(a-x)^4}{(a+4)^4} = \frac{1^4}{2^4}\\\\Powers\ are\ same\ so\ compare\ the\ base\\\\\frac{a-x}{a+x} = \frac{1}{2}\\\\2a - 2x = a + x\\\\2a - a = x + 2x\\\\a = 3x\\\\x = \frac{a}{3}$

Thus value of x is a/3

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