Question-50717

Question Number 50717 by Tawa1 last updated on 19/Dec/18

Answered by tanmay.chaudhury50@gmail.com last updated on 19/Dec/18

x + \sqrt{y} - \sqrt{x} - y = 4

(\sqrt{x} + \sqrt{y}) (\sqrt{x} - \sqrt{y}) - (\sqrt{x} - \sqrt{y}) = 4

(\sqrt{x} - \sqrt{y}) (\sqrt{x} + \sqrt{y} - 1) = 4

b y l o g i c t r i a l x = 9 y = 4 s o z = 1

Commented by Tawa1 last updated on 19/Dec/18

God bless you sir

Answered by ajfour last updated on 19/Dec/18

l e t x + y + z = s

\Rightarrow \sqrt{x} - x = 8 - s

\sqrt{y} - y = 12 - s

\sqrt{z} - z = 14 - s

x - \sqrt{x} + (8 - s) = 0

\sqrt{x} = \frac{1}{2} + \frac{\sqrt{1 + 4 (s - 8)}}{2} (+ v e r o o t)

x = \sqrt{x} + s - 8

= \frac{\sqrt{1 + 4 (s - 8)}}{2} + \frac{1}{2} + s - 8 \dots (i)

s = x + y + z

\Rightarrow 2 s = \sqrt{1 + 4 (s - 8)} + 1 + 2 (s - 8)

+ \sqrt{1 + 4 (s - 12)} + 1 + 2 (s - 12)

+ \sqrt{1 + 4 (s - 14)} + 1 + 2 (s - 14)

\Rightarrow \sqrt{4 s - 31} + \sqrt{4 s - 47} + \sqrt{4 s - 55} + 4 s = 65

\Rightarrow s = 14

A n d f r o m (i)

\Rightarrow x = \frac{\sqrt{1 + 4 (s - 8)}}{2} + \frac{1}{2} + s - 8

\Rightarrow x = 9, y = 4, z = 1 .

Commented by Tawa1 last updated on 19/Dec/18

God bless you sir

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