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Maths-

General

Easy

Question

Evaluate $x squared plus 1 over x squared text if end text x equals 3 plus square root of 8$

hint Hint:

Use rationalisation of denominator.

The correct answer is: 34

Complete step by step solution:
Let $x equals 3 plus square root of 8$
∴ $1 over x equals fraction numerator 1 over denominator 3 plus square root of 8 end fraction equals fraction numerator 1 cross times 3 minus square root of 8 over denominator left parenthesis 3 plus square root of 8 right parenthesis left parenthesis 3 minus square root of 8 right parenthesis end fraction$ (Rationalising the denominator)
$table attributes columnspacing 1em end attributes row cell equals fraction numerator 3 minus square root of 8 over denominator left parenthesis 3 right parenthesis squared minus left parenthesis square root of 8 right parenthesis squared end fraction equals fraction numerator 3 minus square root of 8 over denominator 9 minus 8 end fraction equals fraction numerator 3 minus square root of 8 over denominator 1 end fraction end cell row cell equals 3 minus square root of 8 end cell end table$
Now, $x plus 1 over x equals 3 plus square root of 8 plus 3 minus square root of 8 equals 6$
Squaring both sides, we get $open parentheses x plus 1 over x close parentheses squared equals 6 squared$
$not stretchy rightwards double arrow x squared plus 1 over x squared plus 2 equals 36$
$not stretchy rightwards double arrow x squared plus 1 over x squared equals 36 minus 2 equals 34$

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