If x>0 and x²+1/9x²=25/36, find :x³+1/27x³
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Step-by-step explanation:
x>0 and x²+1/9x²=25/36, find x³+1/27x³. 1. See answer.
Top answer · 16 votes
Given that :x² + 1/9x² = 25/36Adding and subtracting 2/3( x )² + ( 1/3x )² + 2( x )( 1/3x ) - 2/3 = 25/36( x + 1/3x )² = 49/36 ( x + 1/3x ) = 7/6Cubing ... More
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Answer:
The answer is 7/216.
Step-by-step explanation:
x > 0 and x² + 1/9x² = 25 / 36
(x + 1/3x)² = x² + 1/9x² + 2/3 = 25/36 + 2/3
(x + 1/3x)² = 49/36
x + 1/3x = 7/6 , we drop the negative value as x is greater than 0
x³ + 1/27x³ = (x + 1/3x) ( x² + 1/9x² - x/3x)
= 7/6 × (25/36 - 1/3)
= 7/6 × 1/36
= 7/216
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