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Maths-

General

Easy

Question

If $x equals 5 plus 2 square root of 6$ , then find the value of $x squared plus 1 over x squared$

hint Hint:

Hint:
Rationalization is a technique which is used to eliminate the irrational number in the denominator. For example, $fraction numerator 1 over denominator square root of 3 end fraction$ can be rationalised as $fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction$

The correct answer is: 98

Given $x equals 5 plus 2 square root of 6$
Step 1 of 2:
Find the value of x²
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals left parenthesis 5 plus 2 square root of 6 right parenthesis squared end cell row cell x squared equals 25 plus 24 plus 2 cross times 5 cross times 2 square root of 6 end cell row cell x squared equals 49 plus 20 square root of 6 end cell end table$
Step 2 of 2:
Put the value of x² in $x squared plus 1 over x squared$
$x squared plus 1 over x squared equals 49 plus 20 square root of 6 plus fraction numerator 1 over denominator 49 plus 20 square root of 6 end fraction$
Rationalizing $fraction numerator 1 over denominator 49 plus 20 square root of 6 end fraction$ in the upper equation
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 49 plus 20 square root of 6 plus fraction numerator 1 over denominator 49 plus 20 square root of 6 end fraction cross times fraction numerator 49 minus 20 square root of 6 over denominator 49 minus 20 square root of 6 end fraction end cell row cell equals 49 plus 20 square root of 6 plus fraction numerator 49 minus 20 square root of 6 over denominator 49 squared minus left parenthesis 20 square root of 6 right parenthesis squared end fraction end cell row cell equals 49 plus 20 square root of 6 plus fraction numerator 49 minus 20 square root of 6 over denominator 2401 minus 2400 end fraction end cell row cell equals 49 plus 20 square root of 6 plus 49 minus 20 square root of 6 end cell row cell x squared plus 1 over x squared equals 98 end cell end table$
Final Answer:
Hence, the value of $x squared plus 1 over x squared$ is 98.

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