If x 2 + 1/x 2 =14 find x 3 + 1/x 3
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x2 + 1/x2=1Add 2(x)(1/x) on both sides
i.e x2 + 1/x2 + 2(x)(1/x) = 14 + 2(x)(1/x)
x2 +1/x2 +2=14+2
(x + 1/x)2 = (4)2
x + 1/x = 4
now cube on both sides
i.e (x + 1/x)3=(4)3
x3 + 1/x3 + 3(x2)(1/x) + 3(x)(1/x2) = 64
x3 + 1/x3 +3x +3(1/x) =64
x3 + 1/x3 + 3(x+1/x) = 64
x3 + 1/x3 + 3(4) =64
x3 + 1/x3 =52
i.e x2 + 1/x2 + 2(x)(1/x) = 14 + 2(x)(1/x)
x2 +1/x2 +2=14+2
(x + 1/x)2 = (4)2
x + 1/x = 4
now cube on both sides
i.e (x + 1/x)3=(4)3
x3 + 1/x3 + 3(x2)(1/x) + 3(x)(1/x2) = 64
x3 + 1/x3 +3x +3(1/x) =64
x3 + 1/x3 + 3(x+1/x) = 64
x3 + 1/x3 + 3(4) =64
x3 + 1/x3 =52
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