If (a+1/a)^2=3 and a is not equal to 0; then show that:a^3+1/a^3=0
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(a + 1/a)² = 3
(a + 1/a) = √3
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a³ + 1/a³ = ?
a³ + 1/a³ = (a + 1/a)³ - 3(a)(1/a) {a + 1/a}
= (√3)³ - 3 (√3)
= (√3×√3×√3) - 3√3
= 3√3 - 3√3
= 0
Therefore, a³ + 1/a³ = 0
Hope it helps
(a + 1/a) = √3
__________________
a³ + 1/a³ = ?
a³ + 1/a³ = (a + 1/a)³ - 3(a)(1/a) {a + 1/a}
= (√3)³ - 3 (√3)
= (√3×√3×√3) - 3√3
= 3√3 - 3√3
= 0
Therefore, a³ + 1/a³ = 0
Hope it helps
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