Question

find the value of √x-1/√x when X=7+4√3​

Answer 1

Answer:

4

Step-by-step explanation:

$\huge{\blue{\underline{\underline{\mathcal{Answer}}}}}$

x = 7+4√3

x= 4+3 + 2 * 2 * √3

x = 2² +√3 ² + 2* 2* √3 ( a²+b²+2ab)=(a+b)²

x = (2+√3)²

√x = 2+√3

$\frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3 } } \\ \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{ {7}^{2} - {(4 \sqrt{3} })^{2} } \\ \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{49 - 48} \\ \frac{1}{x} = 7 - 4 \sqrt{3}$

1/x = 4+3 - 2*2*√3

1/x = 2² +√3 ² - 2*2*√3 (a²+b²-2ab)=(a-b)²

1/x = (2-√3)²

1/√x = 2-√3 ....

${\underline}$

now.. the value of √x -1/√x

2+√3 - 2-√3

2+2 = 4....

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