if a=x ^1/3 +x^-1/3 then a^3-3a
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Answered by
10
Answer:
Step-by-step explanation:
a = x^(1/3) + x^(−1/3)
a^3 − 3a
= (x^(1/3) + x^(−1/3))^3 − 3 (x^(1/3) + x^(−1/3))
= (x + 3x^(2/3)x^(−1/3) + 3x^(1/3)x^(−2/3) + x^(−1)) − (3x^(1/3) + 3x^(−1/3))
= x + 3x^(1/3) + 3x^(−1/3) + x^(−1) − 3x^(1/3) − 3x^(−1/3)
= x + 1/x
TooFree:
( x + 1/x) is the same as (x + x^-1) written in positive index form.
Answered by
5
= x^(1/3) + x^(-1/3) = x^(-1/3)[x^(2/3) +1]. a^(3) = (1/x)[x^2 + 3x^(4/3) + 3x^(2/3) + 1] = x + 3x^(1/3) + 3x^(-1/3) + 1/x. Then a^3 -3a
x + 3x^(1/3) + 3x^(-1/3) + 1/x - 3x^(1/3) - 3x^(-1/3)
x + 1/x = (x^2 + 1)/x.
hope it will help you
x + 3x^(1/3) + 3x^(-1/3) + 1/x - 3x^(1/3) - 3x^(-1/3)
x + 1/x = (x^2 + 1)/x.
hope it will help you
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