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Question
Solve: `8x^(3/(2"n")) - 8x^((-3)/(2"n"))` = 63
Solution
Put k = `3/(2"n")`
∴ 8xk – 8x-k = 63
`8x^"k" - 8/x^"k"` = 63
8x2k – 8 = 63xk
8x2k – 63xk – 8 = 0
(xk – 8)(8xk + 1) = 0
xk – 8 = 0
xk = 8
`x^(3/(2"n"))` = 8
x = `8^(3/(2"n")) (2^3)^(3/(2"n"))`
= (22)n
= 4n
∴ x = 4n is a root of the equation.
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