x2+1x2=1, find the value of x102+x96+x90+x84+x78+x72+5 (Equation)

Question

x2+1x2=1, find the value of x102+x96+x90+x84+x78+x72+5 (Equation)

Shohan

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2025-01-04 04:42

1 Answers

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Shohan · Accepted Answer · 2024-12-14T13:31:11+06:00

Shohan

$G i v e n t h a t, x^{2} + \frac{1}{x^{2}} = 1 S o, (x^{2} + \frac{1}{x^{2}}) (x + \frac{1}{x}) = (x + \frac{1}{x}) [M u l t i p l y i n g b o t h s i d e s b y (x + \frac{1}{x})] = x^{3} + x + \frac{1}{x^{3}} = (x + \frac{1}{x}) ∴ x^{3} + \frac{1}{x^{3}} = 0 N o w, x^{102} + x^{96} + x^{90} + x^{84} + x^{78} + x^{72} + 5 x^{99} (x^{3} + \frac{1}{x^{3}}) + x^{87} (x^{3} + \frac{1}{x^{3}}) + x^{75} (x^{3} + \frac{1}{x^{3}}) + 5 = 0 + 0 + 5 = 5 A n s w e r : 5$

9 views Answered 2024-12-14 13:31