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Maths-

General

Easy

Question

If $x equals 2 plus square root of 3$ find the values 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: 14

Given x = $2 plus square root of 3$
Step 1 of 2:
Find the value of x²
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals left parenthesis 2 plus square root of 3 right parenthesis squared end cell row cell x squared equals 4 plus 3 plus 2 cross times 2 cross times square root of 3 end cell row cell x squared equals 7 plus 4 square root of 3 end cell end table$
Step 2 of 2:
Put the value of x² in $x squared plus 1 over x squared$
$x squared plus 1 over x squared equals 7 plus 4 square root of 3 plus fraction numerator 1 over denominator 7 plus 4 square root of 3 end fraction$
Rationalizing $fraction numerator 1 over denominator 7 plus 4 square root of 3 end fraction$ in the upper equation
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 7 plus 4 square root of 3 plus fraction numerator 1 over denominator 7 plus 4 square root of 3 end fraction cross times fraction numerator 7 minus 4 square root of 3 over denominator 7 minus 4 square root of 3 end fraction end cell row cell equals 7 plus 4 square root of 3 plus fraction numerator 7 minus 4 square root of 3 over denominator 49 minus 48 end fraction end cell row cell equals 7 plus 4 square root of 3 plus 7 minus 4 square root of 3 end cell row cell x squared plus 1 over x squared equals 14 end cell end table$
Final Answer:
Hence, the value of $x squared plus 1 over x squared$ is 14

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