If a-1/a=4, find the value of a³-1/a³
Answers
Answered by
16
Step-by-step explanation:
a-1/a=4
square on both sides
(a-1/a)²=4²
a²+1/a²-2a.1/a=16
a²+1/a²-2=16
a²+1/a²=14
a³-b³=(a-b)(a²+b²+ab)
using this formula we get
a³-1/a³ = (a-1/a)(a²+1/a²+a.1/a)
=4(14+1)
=4*15=60
Answered by
3
a³- 1/a³ = 60
given,
a-1/a = 4
squaring both side
(a-1/a)² = 4²
a²+1/a²-2(a) (1/a) = 16
a²+1/a²-2=16
a²+1/a²=16+2
a²+1/a²= 18
a³-b³=(a-b) (a²+b²+ab)
a³-1/a³=(a-1/a) (a²+1/a²+a×1/a)
=4(14+1)
=4×15
=60
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