Question

If 3x-4/x=4 find 27x^3-64/x^3

Answer 1

identity

=> (a³+b³ ) = (a+b)(a²+ab+b²)

according to question

3x - 4/x = 4 ......(1)

take both side square

=> 9x² + 16/x² - 24 = 16

=> 9x² + 16/x² = 40 ......(2)

then

=> 27x³ - 64/x³

= (3x)³ - (4/x)³

= (3x + 4/x) (9x² + 16/x² + 12)

put the value from equation (1) & (2)

= 4 (40 +12)

= 4×52

= 208

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