If x 3 +1/x 3 =110, then find the value of x+1/x.
Answers
Answered by
4
x³ + 1/x³ = 110
(x+1/x)(x²–x•1/x+1/x²) = 110
(x+1/x)(x²+1/x²–1) = 110
(x+1/x)((x+1/x)²–3) = 110
Let y = x+1/x
y(y²–3) = 110
y³–3y–110 = 0
(y–5)(y²+5y+22) = 0
y–5 = 0 or y²+5y+22 = 0
y = 5
x+1/x = 5
(x+1/x)(x²–x•1/x+1/x²) = 110
(x+1/x)(x²+1/x²–1) = 110
(x+1/x)((x+1/x)²–3) = 110
Let y = x+1/x
y(y²–3) = 110
y³–3y–110 = 0
(y–5)(y²+5y+22) = 0
y–5 = 0 or y²+5y+22 = 0
y = 5
x+1/x = 5
Similar questions