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

hintHint:

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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