Question-191962

Question Number 191962 by ajfour last updated on 04/May/23

Answered by mr W last updated on 04/May/23

{[\sqrt{{(a + x)}^{2} - {(a - x)}^{2}} - \sqrt{{(a + b)}^{2} - {(a - b)}^{2}}]}^{2} = {(b + x)}^{2} - {(2 a - b - x)}^{2}

{[\sqrt{a x} - \sqrt{a b}]}^{2} = 2 a (x - a + b)

x + 2 \sqrt{b x} - 2 a + b = 0

\Rightarrow \sqrt{x} = - \sqrt{b} + \sqrt{2 a}

\Rightarrow x = {(\sqrt{2 a} - \sqrt{b})}^{2} = 2 a + b - 2 \sqrt{2 a b}

Commented by mr W last updated on 04/May/23

i n t e r e s t i n g!

Commented by ajfour last updated on 05/May/23

{(2 \sqrt{a x} - 2 \sqrt{a b})}^{2} = 4 a (x + b - a)

{(\sqrt{x} - \sqrt{b})}^{2} = x + b - a

\Rightarrow a = 2 \sqrt{b x}

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