Question
If x4 – 62x2 + 1 = 0, then a
value of x 3 + x -3 can be:Solution
x4 – 62x2 + 1 = 0 Divide by x2 x2 – 62 + 1/x2 = 0 ⇒ x2 + 1/x2 = 62 As we know, (x + 1/x)2 = x2 + 1/x2 + 2 ⇒ (x + 1/x)2 = 62 + 2 = 64 ⇒ x + 1/x = √64 = 8 Again, As we know, (x + 1/x)3 = x3 + 1/x3 + 3 (x + 1/x) ⇒ 83 = x3 + 1/x3 + 3 × 8 ⇒ x3 + 1/x3 = 512 – 24 = 488
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