If-x-a-2b-a-2b-a-2b-a-2b-then-the-value-of-bx-2-ax-b-is-

Question Number 112805 by Aina Samuel Temidayo last updated on 09/Sep/20

If x = \frac{\sqrt{a + 2 b} + \sqrt{a - 2 b}}{\sqrt{a + 2 b} - \sqrt{a - 2 b}}, then the value

of {bx}^{2} - ax + b is

Answered by nimnim last updated on 09/Sep/20

\frac{x}{1} = \frac{\sqrt{a + 2 b} + \sqrt{a - 2 b}}{\sqrt{a + 2 b} - \sqrt{a - 2 b}}

\Rightarrow \frac{x + 1}{x - 1} = \frac{2 \sqrt{a + 2 b}}{2 \sqrt{a - 2 b}} (by componendo & dividendo)

\Rightarrow \frac{x^{2} + 2 x + 1}{x^{2} - 2 x + 1} = \frac{a + 2 b}{a - 2 b}

\Rightarrow \frac{2 (x^{2} + 1)}{4 x} = \frac{2 a}{4 b} (by componendo & dividendo)

\Rightarrow \frac{x^{2} + 1}{x} = \frac{a}{b}

\Rightarrow {bx}^{2} + b = ax

\Rightarrow {bx}^{2} - ax + b = 0 ★

Commented by Aina Samuel Temidayo last updated on 09/Sep/20

Ok . Thanks .