Question

If 3x + 2y = 12 and xy = 6, then find 27x 3 +8y 3

Answer 1

Ello!!

Here's your answer

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Given , 3x + 2y = 12 and xy = 6

To find the value of ( 27x^3 + 8y^3 )

Now , ( 27x^3 + 8y^3 )

= ( 3x )^3 + ( 2y )^3

= ( 3x + 2y ) { ( 3x )^2 - 3x × 2y + ( 2y )^2 }

[ • ( a )^3 + ( b )^3 = ( a + b ) ( a^2 + ab + b^2 ) → Using this identity ]

= 12 × { ( 3x )^2 + ( 2y )^2 - 6 × 6 } [ • Putting the values ]

= 12 { ( 3x + 2y ) - 2 * 3x * 2y - 36 }

[ • ( a )^2 + ( b )^2 = ( a + b )^2 - 2ab → Using this identity ]

= 12 { 12 - 12 × 6 - 36 }

= 12 × ( 12 - 72 - 36 )

= 12 × ( - 96 )

= - 1152

So , the value of the following is - 1152

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Hope it helps you dear!

★ Devil king