Question

1/(3 - sqrt(8)) - 1/(sqrt(8) - sqrt(7)) + 1/(sqrt(7) - sqrt(6)) - 1/(sqrt(6) - sqrt(5)) + 1/(sqrt(7) - 6) = 5
please tell me correct answer​

Answer 1

The correct question is, " Find the value of  $\bf \frac{1}{3-\sqrt{8} } -\frac{1 }{\sqrt{8}-\sqrt{7} } +\frac{1}{\sqrt{7}-\sqrt{6}} -\frac{1}{\sqrt{6}-\sqrt{5}} +\frac{1}{\sqrt{5}-{2}}$ ".

The answer is 1.

$\frac{1}{3-\sqrt{8} } -\frac{1 }{\sqrt{8}-\sqrt{7} } +\frac{1}{\sqrt{7}-\sqrt{6}} -\frac{1}{\sqrt{6}-\sqrt{5}} +\frac{1}{\sqrt{5}-{2}}$

After rationalizing the terms, we get

$\frac{1}{3-\sqrt{8} }=3+\sqrt{8}$

$\frac{1 }{\sqrt{8}-\sqrt{7} } =\sqrt{8}+\sqrt{7}$

$\frac{1 }{\sqrt{7}-\sqrt{6} } =\sqrt{7}+\sqrt{6}$

$\frac{1 }{\sqrt{6}-\sqrt{5} } =\sqrt{6}+\sqrt{5}$

$\frac{1 }{\sqrt{5}-2 } =\sqrt{5}+2$

By substituting these values, we get

$\frac{1}{3-\sqrt{8} } -\frac{1 }{\sqrt{8}-\sqrt{7} } +\frac{1}{\sqrt{7}-\sqrt{6}} -\frac{1}{\sqrt{6}-\sqrt{5}} +\frac{1}{\sqrt{5}-{2}}=3+\sqrt{8}-[\sqrt{8} +\sqrt{7}]+[\sqrt{7}+\sqrt{6}]-[\sqrt{6}+\sqrt{5} ]+[\sqrt{5}-2 ] \\\\\frac{1}{3-\sqrt{8} } -\frac{1 }{\sqrt{8}-\sqrt{7} } +\frac{1}{\sqrt{7}-\sqrt{6}} -\frac{1}{\sqrt{6}-\sqrt{5}} +\frac{1}{\sqrt{5}-{2}}=3-2=1$

Hence the value of the given function is 1.

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