Question

find value of 27x3+8y3 if 3x+2y=20 and xy 11÷9​

Answer 1

27x^3+8y^3

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

using identitya^3+b^3=(a+b)(a^2+b^2+ab

(3x+2y)[(3x)^2+(2y)^2+(3x)(2y)]

but 3x+2y=20 (given)

20[(3x)^2+(2y)^2+6xy]

using identity a^2+b^2=(a+b)^2-2ab

20[(3x+2y)^2-2(3x)(2y)+6xy]

again 3x+2y=20

20[(20)^2-12xy+6xy]

20[400+6xy]

but xy =11/9

20[400+6(11/9)]

20[400+22/3]

20[400+7.33]

20(407.33)

8146.66(approximately)

hope it will help you