2-x-3-x-3-x-4-x-2-x-4-x-x-2-

Question Number 159587 by cortano last updated on 19/Nov/21

\sqrt{2 - x} \sqrt{3 - x} + \sqrt{3 - x} \sqrt{4 - x} + \sqrt{2 - x} \sqrt{4 - x} = x + 2

Commented by mr W last updated on 19/Nov/21

w e c a n u s e m y m e t h o d i n Q 159527

f o r s o l v i n g t h i s k i n d o f e q u a t i o n s .

Answered by mr W last updated on 19/Nov/21

{(\sqrt{2 - x} + \sqrt{3 - x} + \sqrt{4 - x})}^{2} = 2 - x + 3 - x + 4 - x + 2 (\dots L H S \dots)

{(\sqrt{2 - x} + \sqrt{3 - x} + \sqrt{4 - x})}^{2} = 9 - 3 x + 2 (x + 2)

{(\sqrt{2 - x} + \sqrt{3 - x} + \sqrt{4 - x})}^{2} = 13 - x

\sqrt{2 - x} + \sqrt{3 - x} + \sqrt{4 - x} = \sqrt{13 - x}

\sqrt{2 - x} + \sqrt{3 - x} = \sqrt{13 - x} - \sqrt{4 - x}

{(\sqrt{2 - x} + \sqrt{3 - x})}^{2} = {(\sqrt{13 - x} - \sqrt{4 - x})}^{2}

2 - x + 3 - x + 2 \sqrt{(2 - x) (3 - x)} = 13 - x + 4 - x - 2 \sqrt{(13 - x) (4 - x)}

\sqrt{(2 - x) (3 - x)} = 6 - \sqrt{(13 - x) (4 - x)}

(2 - x) (3 - x) = 36 + (13 - x) (4 - x) - 12 \sqrt{(13 - x) (4 - x)}

6 - 5 x + x^{2} = 36 + 52 - 17 x + x^{2} - 12 \sqrt{(13 - x) (4 - x)}

41 - 6 x = 6 \sqrt{(13 - x) (4 - x)}

{(41 - 6 x)}^{2} = 36 (13 - x) (4 - x)

120 x = 191

\Rightarrow x = \frac{191}{120}

Commented by cortano last updated on 19/Nov/21

n i c e

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