a^2+1/a^2 = 18 find : a^3- 1/ a^3
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Solution:
a²+1/a² = 18 ----(1)
subtract 2 from both sides of the equation, we get
a²+1/a²-2=18-2
=> (a-1/a)² = 16
=> a-1/a = √16
=> a - 1/a = 4 ---(2)
Now ,
a³ - 1/a³
= (a-1/a)[ a²+a*1/a+b²]
= (a-1/a)[a²+b²+1]
= 4×(18+1)
= 4×19
= 76
Therefore,
a³-1/a³ = 76
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