If x + 1/x = 83, find the value of x^2 + 1/x^2

Chen Houwu asked Oct 28, 2023

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37 votes

Chen Houwu asked Oct 28, 2023

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21 votes

Answer:

6887

Explanation:

given

x +
(1)/(x) = 83 ( square both sides )

(x +
(1)/(x) )² = 83² = 6889 ← expand factor on left using FOIL

x² + 2( x ×
(1)/(x) ) +
(1)/(x^2) = 6889

x² + 2(1) +
(1)/(x^2) = 6889 ( subtract 2 from both sides )

x² +
(1)/(x^2) = 6887

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