Question

2x+3y=13
Xy= 6
Find 8x³+27y³=(13)³

Answer 1

First of all, thanks for asking this question.

Here is your answer:

Given: 2x + 3y = 13 and xy = 6.

(Cubing on both sides, we get)

We know that (a+b)^3 = a^3 + b^3 + 3ab(a+b).  

                    (2x + 3y)^3 = (2x)^3 + (3y)^3 + 3(2x)(3y)(2x + 3y) = (13)^3  

                                        8x^3 + 27y^3 + 18xy(13) = 2197      

                                    8x^3 + 27y^3 + 18(6)(13) = 2197      

                                   8x^3 + 27y^3 + 1404 = 2197

                                         8x^3 + 27y^3 = 2197 - 1404      

                                                            = 793

                                 Therefore 8x^3 + 27y^3 = 793.

Hope this helps!

Be Brainly!

Answer 2

8x³+27y³ = 793

Step-by-step explanation:

Given that 2x+3y = 13 or xy = 6

2x+3y = 13

Cubic both sides

$(2x+3y)^3=(13)^3\\(2x)^3+(3y)^2+3\times2x\times3y(2x+3y)=(13)^3\\8x^3+27y^3+18xy(13)=13^3\\8x^3+27y^3+234xy=2197\\8x^3+27y^3+234xy-2197=0\\8x^3+27y^3+234\times6-2197=0\\8x^3+27y^+1404-2197=0\\8x^3+27y^3=793$