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प्रश्न
Simplify the following:
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
उत्तर
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
= `"a"^(1/3)("a"^(2/3) -1 + "a"^(-2/3)) + "a"^(-1/3)("a"^(2/3) - 1 + "a"^(-2/3))`
= `("a"^(1/3) xx "a"^(2/3) - "a"^(1/3) xx 1 + "a"^(1/3) xx "a"^(-2/3)) + ("a"^(-1/3) xx "a"^(2/3) - "a"^(-1/3) xx 1 + "a"^(-1/3) xx "a"^(-2/3))`
= `("a"^(1/3 + 2/3) - "a"^(1/3) xx 1 + "a"^(1/3 + 2/3)) + ("a"^(-1/3 + 2/3) - "a"^(-1/3) + "a"^(-1/3 - 2/3))` .....(Using am x an = am+n)
= `("a"^1 - "a"^(1/3) + "a"^(-1/3)) + ("a"^(1/3) - "a"^(-1/3) + "a"^-1)`
= `"a" - "a"^(1/3) + "a"^(-1/3) + "a"^(1/3) - "a"^(-1/3) + (1)/"a"`
= `"a" + (1)/"a"`.
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