Question

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

Answer 1

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