x-1/x=√2 find x=1/x find a) x²+1/x² b)x+1/x c)x³+1/x³
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Answer:
a) 4 b) c) 3
Step-by-step explanation:
a) x-1/x =
(x-1/x)^2 = x^2+1/x^2-2
()^2+2 = x^2+1/x^2
2+2 = x^2+1/x^2
x^2+1/x^2 = 4
b)(x+1/x)^2 = x^2+1/x^2+2
x+1/x =
x+1/x =
c) (x+1/x)^3 = x^3+1/x^3+3(x+1/x)
()^3 = x^3+1/x^3+3
6-3 = x^3+1/x^3
x^3+1/x^3 = 3
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