Question

$If \: x < 0 \: and \: {x}^{2} + \frac{1}{ {9x}^{2} } = \frac{25}{36} \\ \\ \\ Find: {x}^{3} + \frac{1}{ {27x}^{3} }$

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Answer 1

Hey !!

x²+ 1/9x²

=> x²+ 1/(3x)² = 25/36 ------1)

=> x² + 1/3x² = (x+ 1/3x)²-2x×1/3x

=> 25/36 = (x+ 1/3x)² - 2/3

=> 25/36 + 2/3 = (x + 1/3x)²

=> 25 + 24/36 = (x+1/3x)²

=> 49/36 = (x + 1/3x)²

=> 7/6 = (x+ 1/3x) --------2)

Now ..We want to find

x³ + 1/27x³ = ¿?

x³ + 1/(3x)³

we know a formula a³ + b³
= (a + b) ( a²+ b ² - ab )

like that ..

{(x + 1/3x )(x² + (1/3x)²-x×1/3x }

=> (7/6) ( 25/36 - 1/3 )

[putting value from 1 ) and 2 equation



=> 7/6 ( 25 - 12 /36)

=> 7/6 × 13/36

=> 7×13/36*6

=> 91/216 Answer

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Hope it helps you !!

@Rajukumar111

Answer 2

Answer:

This is the answer for the question dear maths aryabatta sir/ mam