Question

If x +1/x = 1.5 find i) x^2+1/x^2
ii) x^4+1/x^4
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Answer 1

Answer:

(i) 0.25

(ii) - 1.9375

Step-by-step explanation:

(i)

x + 1/x = 1.5

taking square both sides

(x + 1/x)² = 1.5²

x² + 1/x² + 2 = 2.25

x² + 1/x² = 2.25 - 2

x² + 1/x² = 0.25

(ii)

x² + 1/x² = 0.25

taking square both sides

(x² + 1/x²)² = 0.25²

x⁴ + 1/x⁴ + 2 = 0.0625

x⁴ + 1/x⁴ = 0.0625 - 2

x⁴ + 1/x⁴ = - 1.9375