Question

1+x=√3(1-x) then what is x value

Answer 1

Step-by-step explanation:

1+x = √3(1-x)

1+x²+2x = 3(1+x²-2x)

1+x²+2x = 3+3x²-6x

2x² - 8x + 2 = 0

x² - 4x + 1 = 0

x = 4 + √16-4 / 2

x = 4 + √12 / 2

x = 4 + 2√3 / 2

x = 2 + √3

Answer 2

Answer:

$\red { Value \: of \: x } \green {= 2-\sqrt{3}}$

Step-by-step explanation:

$Given \:1 + x = \sqrt{3} ( 1-x)$

$\implies 1 + x = \sqrt{3} - \sqrt{3}x$

$\impliee x + \sqrt{3}x = \sqrt{3} - 1$

$\implies x( 1 + \sqrt{3} ) = \sqrt{3} - 1$

$\implies x = \frac{(\sqrt{3} - 1 )}{(\sqrt{3}+1)}$

$= \frac{(\sqrt{3} - 1 )(\sqrt{3} - 1)}{(\sqrt{3}+1)(\sqrt{3} - 1)}$

$= \frac{(\sqrt{3} - 1)^{2}}{(\sqrt{3})^{2} - 1 }$

$= \frac{ (\sqrt{3})^{2} + 1^{2} - 2\sqrt{3}\times 1}{(\sqrt{3})^{2} - 1^{2}}$

$= \frac{3+1-2\sqrt{3} }{3-1}$

$= \frac{4 - 2\sqrt{3}}{2}\\= \frac{2(2-\sqrt{3})}{2}$

$= 2-\sqrt{3}$

Therefore.,

$\red { Value \: of \: x } \green {= 2-\sqrt{3}}$

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