A2+1/a=4,find 2a3+2/a3
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a +1/a = 4
a² + 1/a² = (a+1/a)² - 2 = (4)² -2 = 16 -2 = 14
now,
2a³ +2/a³ = 2(a³ +1/a³)
we know that, (a³ +b³) = (a+b)(a² -ab+b²)
=2(a+1/a)(a² - 1 + 1/a²)
=2×4×(14-1) =8×13 = 104
a² + 1/a² = (a+1/a)² - 2 = (4)² -2 = 16 -2 = 14
now,
2a³ +2/a³ = 2(a³ +1/a³)
we know that, (a³ +b³) = (a+b)(a² -ab+b²)
=2(a+1/a)(a² - 1 + 1/a²)
=2×4×(14-1) =8×13 = 104
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