Question
x^2 + 1/x^2 = 47. find the value of x+ 1/x and x- 1/x
Answers
Steve
(x + 1/x)^2 = x^2 + 2 + 1/x^2
(x - 1/x)^2 = x^2 - 2 + 1/x^2
So, letting
u = x + 1/x
v = 1 - 1/x
u^2 + v^2 = 2(x^2 + 1/x^2) = 98
u^2 - v^2 = 4
u^2 = 49
v^2 = 45
x + 1/x = ±7
x - 1/x = ±3√5
(x - 1/x)^2 = x^2 - 2 + 1/x^2
So, letting
u = x + 1/x
v = 1 - 1/x
u^2 + v^2 = 2(x^2 + 1/x^2) = 98
u^2 - v^2 = 4
u^2 = 49
v^2 = 45
x + 1/x = ±7
x - 1/x = ±3√5
Steve
oops. 94, not 98