if x^2+1/x^2 =146 find x^3-1/x^3
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x²+1/x² = 146
(x)² + (1/x)² = 146
x²+(1/x)²+ 2(x)(1/x) - 2(x)(1/x) = 146
(x-1/x)²+2 = 146
(x-1/x)² = 146-2
x-1/x = √144
x-1/x = 12
(a³-b³)= (a-b)(a²+ab+b²)
(x³-(1/x)³) = (x-1/x)[x²+(x)(1/x)+(1/x)²]
→ (x³-1/x³) = (12)(x²+1+1/x²)
→ (x³-1/x³) = (12)(146+1) {x²+1/x² = 146}
→ (x³-1/x³) = 12(147) = 1764
Hope it helps
(x)² + (1/x)² = 146
x²+(1/x)²+ 2(x)(1/x) - 2(x)(1/x) = 146
(x-1/x)²+2 = 146
(x-1/x)² = 146-2
x-1/x = √144
x-1/x = 12
(a³-b³)= (a-b)(a²+ab+b²)
(x³-(1/x)³) = (x-1/x)[x²+(x)(1/x)+(1/x)²]
→ (x³-1/x³) = (12)(x²+1+1/x²)
→ (x³-1/x³) = (12)(146+1) {x²+1/x² = 146}
→ (x³-1/x³) = 12(147) = 1764
Hope it helps
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