Question

if 3x + 2y = 12 and xy=6 find the value of 27x³+8y³

Answer 1

your answer is in attachment. you can ask more

e8b8b95957fbe74bc72b1eab473a3be8.docx

Answer 2

3x+2y=12 and xy=6
 ( 3x )^3+( 2y )^3=( 3x+2y ) [( 3x )^2+( 2y )^2-xy ].        ⇒27x^3+8y^3=12( 9x^2+4y^2-6 )
and now, we have to find out the value of, 9x^2+4y^2
∴( 3x+2y )^2=( 3x )^2+( 2y )^2 +2( 3x )( 2y )
⇒( 12 )^2=9x^2+4y^2+12*6
⇒144=9x^2+4y^2+72
⇒144-72=9x^2+4y^2
⇒132=9x^2+4y^2
∴27x^3+8y^3=12(132-6)
⇒27x^3+8y^3=126.
hope that it will help.