If-x-1-x-2-y-1-y-2-1-then-find-x-y-2-

Question Number 206063 by MATHEMATICSAM last updated on 06/Apr/24

If (x + \sqrt{1 + x^{2}}) (y + \sqrt{1 + y^{2}}) = 1 then

find {(x + y)}^{2} .

Answered by mr W last updated on 06/Apr/24

x + \sqrt{1 + x^{2}} = - y + \sqrt{1 + {(- y)}^{2}}

f (x) = x + \sqrt{1 + x^{2}} i s s t r i c t l y i n c r e a s i n g .

i f f (a) = f (b), t h e n a = b .

\Rightarrow x = - y

\Rightarrow x + y = 0 \Rightarrow {(x + y)}^{2} = 0

Answered by Berbere last updated on 06/Apr/24

y = s h (t) = x = s h (w)

(s h (w) + c h (w)) (s h (t) + c h (t)) = 1

e^{w} . e^{t} = 1

w + t = 0

x + y = s h (w) + s h (- w) = 0

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