If x=3 find the value of (x^1/3+x^-1/3)(x^2/3+x^-2/3-1)
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we will use the formula
(a+b)(a²+b²-ab)=a³+b³
so we have,
(x^1/3+x^-1/3)(x^2/3+x^-2/3-1)
=[(x^1/3)+(x^-1/3)][(x^1/3)²+(x^-1/3)²-(x^1/3)(x^-1/3)]
considering,
x^1/3=a and
x^-1/3=b
the given expression becomes
(x^1/3)³+(x^-1/3)³
=(x^1)+(x^-1)
=x+(1/x)
=3+(1/3)
=10/3
(a+b)(a²+b²-ab)=a³+b³
so we have,
(x^1/3+x^-1/3)(x^2/3+x^-2/3-1)
=[(x^1/3)+(x^-1/3)][(x^1/3)²+(x^-1/3)²-(x^1/3)(x^-1/3)]
considering,
x^1/3=a and
x^-1/3=b
the given expression becomes
(x^1/3)³+(x^-1/3)³
=(x^1)+(x^-1)
=x+(1/x)
=3+(1/3)
=10/3
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