Math, asked by nahimalum, 1 year ago

Find x if \frac{\sqrt {3x+1} +\sqrt {3x-6}}{\sqrt {3x+1}-\sqrt {3x-6}}=7

Answers

Answered by shadowsabers03
0
\frac{\sqrt{3x + 1} + \sqrt{3x - 6}}{\sqrt{3x + 1} - \sqrt{3x - 6}} = \frac{7}{1}

If \frac{a}{b} = \frac{c}{d} , then \frac{a + b}{a - b} = \frac{c + d}{c - d}

∴ \frac{(\sqrt{3x + 1} + \sqrt{3x - 6}) + (\sqrt{3x + 1} - \sqrt{3x - 6})}{(\sqrt{3x + 1} + \sqrt{3x - 6}) - (\sqrt{3x + 1} - \sqrt{3x - 6})} = \frac{7 + 1}{7 - 1} \\ \\ = \frac{\sqrt{3x + 1} + \sqrt{3x - 6} + \sqrt{3x + 1} - \sqrt{3x - 6}}{\sqrt{3x + 1} + \sqrt{3x - 6} - \sqrt{3x + 1} + \sqrt{3x - 6}} = \frac{8}{6} \\ \\ = \frac{2\sqrt{3x + 1}}{2\sqrt{3x - 6}} = \frac{4}{3} \\ \\ = \frac{\sqrt{3x + 1}}{\sqrt{3x - 6}} = \frac{4}{3} \\ \\ (\frac{\sqrt{3x + 1}}{\sqrt{3x - 6}})^2 = (\frac{4}{3})^2  

= \frac{3x + 1}{3x - 6} = \frac{16}{9} \\ \\ \\ 9(3x + 1) = 16(3x - 6) \\ = 27x + 9 = 48x - 96 \\ 48x - 27x = 96 + 9 \\ = 21x = 105 \\ \\ x = \frac{105}{21} = 5  

5 is the answer. 

Hope this will be helpful. 
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