Question

3x +2y=9, xy = 3
find 27x3 + 8y3​

Answer 1

Answer:

✅Here's your answer

#(a) ^3 +(b) ^3 = (a+b) (a^2 -ab+b^2)

✔Given : 3x +2y=9 , xy =3

So

$(3x) ^{3} + {2y}^{3} = (3x + 2y)(9 {x}^{2} - 6xy + \\ 4 {y}^{2} ) \\ \\ \\ 27 {x}^{3} + 8 {y}^{3} = (9)(9{x}^{2} - 18 + 4 {y}^{2} ) \\ \\ 27 {x}^{3} + 8 {y}^{3} = 81 {x}^{2} - 162 + </strong><strong>3</strong><strong>6</strong><strong>{y}^{2}$

Answer 2

Answer

3x + 2y = 9

xy = 3

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

[Identity: (a + b)^3 = a^3 + b^3 + 3ab(a + b)]

=> 9^3 = 27x^3 + 8y^3 + 3(6xy)(9)

=> 729 = 27x^3 + 8y^3 + 27(6×3)

=> 729 - 486 = 27x^3 + 8y^3

=> 27x^3 + 8y^3 = 243