Question

x^2+1/x^2=62 'then find value of x^3+1/x^3

Answer 1

Given ;

• x² + 1/x² = 62
• (x+1/x)² - 2(x)(1/x) = 62. { using a² + b² = (a+b)² - 2ab }
• ( x + 1/x )² = 62 + 2
• x + 1/x = √64
• x + 1/x = 8. { eq.1 }

=> From (eq.1)³

• ( x + 1/x )³ = 512
• x³ + 1/x³ + 3( x + 1/x )( x × 1/x ) = 512. { identity used }
• x³ + 1/x³ + 3(8) = 512 (from eq.1)
• x³ + 1/x³ = 512 - 24
• x³ + 1/x³ = 488

#answerwithquality

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