Question

x^2+1/9x^2=25/36 find x^3+1/27x^3

Answer 1

Hi ,

x² + 1/9x² = 25/36

x² + ( 1/3x )² = 25/36

x² + ( 1/3x )² + 2 × x × ( 1/3x ) = 25/36 + 2/3

( x + 1/3x )² = ( 25 + 24 ) / 36

( x + 1/3x )² = 49/36

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

Now ,

x³ + 1/27x³

= x³ + ( 1/3x )³

= ( x + 1/3x )³ - 3 × x × ( 1/3x ) [ x + 1/3x ]

= ( x + 1/3x )³ - ( x + 1/3x )

= ( 7/6 )³ - 7/6

= 7/6 [ (7/6)² - 1 ]

= 7/6 ( 49/36 - 1 )

= 7/6 [ 49 - 36 ] / 36

=( 7 × 13) / 216

= 91/216

I hope this helps you.

: )

Answer 2

Given Equation is x^2 + 1/9x^2 = 25/36.

We know that (x + 1/3x)^2 = x^2 + 1/9x^2 + 2 * x * 1/3x

                                            = x^2 + 1/9x^2 + 2/3

                                           = 25/36 + 2/3

                                           = 25 + 2* 12/36

                                           = 25 + 24/36

                                           = 49/36


                                x + 1/3x = 7/6.


Now,

On cubing both sides, we get

(x + 1/3x)^3 = (7/6)^3

x^3 + 1/27x^3 + 3 * x^2 * 1/3x + 3 * x * 1/9x^2 = 343/216

x^3 + 1/27x^3 + x + 1/3x = 343/216

x^3 + 1/27x^3 + 7/6 = 343/216

x^3 + 1/27x^3 = 343/216 - 7/6

x^3 + 1/27x^3 = (343 - 7 * 36)/(216)

x^3 + 1/27x^3 = 91/216.



Hope this helps!