Question

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

Answer 1

cube both sides
(3x+2y)^3=(12)^3
27x^3+8x^3+3(3x)(2y)(3x+2y)=1728
27x^3+8y^3+18xy(12)=1728
27x^3+8y^3+108(12)=1728
27x^3+8y^3+1296=1728
27x^3+8y^3=1728-1296
27x^3+8y^3=432

Answer 2

27x³ + 8y³

= (3x)³ + (2y)³

a³ + b³ = (a + b)(a² - ab + b²)

Given,

3x + 2y = 12 and xy = 6

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

= 12 {(3x)² - 6xy + (2y)²}

= 12 {(3x)²-6(6)+(2y)²}

= 12 {(3x)²+(2y)² - 36}

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

= 12 {(3x+2y)² - 12xy - 36

= 12 {(12)²-12(6)-36}

= 12 {144-72-36}

= 12 {36}

= 432

Hope it helps...,