Question

If (x-1/5)=5,find the value of (a)x^2+1/x^2, and (b) x^4+1/x^4

Answer 1

Correct Question :- If (x-1/x)=5, find the value of (a)x^2+1/x^2, and (b) x^4+1/x^4 ?

Solution :-

→ (x - 1/x) = 5

Squaring both sides we get,

→ (x - 1/x)² = 5²

using (a - b)² = a² + b² - 2ab in LHS now,

→ x² + 1/x² - 2 * x * 1/x = 25

→ x² + 1/x² - 2 = 25

→ x² + 1/x² = 25 + 2

→ (x² + 1/x²) = 27 (Ans.) (a)

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Now,

→ (x² + 1/x²) = 27

Squaring both sides we get,

→ (x² + 1/x²)² = 27²

using (a + b)² = a² + b² + 2ab in LHS now,

→ x⁴ + 1/x⁴ + 2 * x² * 1/x² = 729

→ x⁴ + 1/x⁴ + 2 = 729

→ x⁴ + 1/x⁴ = 729 - 2

→ (x⁴ + 1/x⁴) = 727 (Ans.) (B)