Question

Find 8x³ + 27y³ if 2x + 3y =13 and xy=6

Answer 1

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!

Answer 2

Answer:

We have,

(2x + 3y) = 13

Cubing on both the sides

=> (2x + 3y)³ = 13³

=> (2x)³ + (3y)³ + 3 × 2x × 3y (2x + 3y) = 13³

Now, by solving this equation

=> 8x³ + 27y³ + 18xy (2x + 3y) = 2197

=> 8x³ + 27y³ + 18 × 6 × 13 = 2197

=> 8x³ + 27y³ + 1404 = 2197

=> 8x³ + 27y³ = 2197 - 1404

= 793

Hence, the value of 8x³ + 27y³ is 793.