To show that x^{2}+\frac{1}{x^{2}}=34 when x=3-2\sqrt{2}.

Michelle Isakson

Michelle Isakson

Answered question

2021-11-06

To show that x2+1x2=34 when x=322.

Answer & Explanation

Drood1980

Drood1980

Beginner2021-11-07Added 16 answers

Calculation:
PSKx2+1x2=34
Let us consider the Right-hand side part of the equation:
x2+1x2
Replacing the value of x in the equation, we get
(322)2+1(322)2
=32+(22)282+132+(22)282
=9+882+19+882
=1782+11782
=(1782)2+11782
=172+(82)22×17×82+1
=34
Hence LHS is equal to RHS.
Conclusion:
Hence, x2+1x2=34 when x=322.

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