if x>0 and x^2+1/9x^2 =25/36, find:x^3+1/27x^3.

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Solution

X²+(1÷9x²) = 25÷36
x² + ( 1÷3x)² + 2 × x × (1÷3x) = 25÷36 + 2÷3
(x+(1÷3x))² = 49÷36
x+(1÷3x) = 7÷6
x³ + (1÷27x³) = (x + (1÷3x))×(x² – (1÷3) + (1÷3x) ²)
= (7÷6) × ((25÷36) – (1÷3))
= (7/6)×(13/36)
= 91/216

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