Question

if 2x+3y= 13 andxy=6 find 8 x cube + 27 y cube

Answer 1

2x+3y=3 - eqn1
xy=6 - eqn2
.: x=6/y
Putting in eqn 1
.: (12/y) + 3y =13
Multiply by y,
.: 12+3y²=13y
.: 3y²-13y+12=0
Solving the equation,
We get, y=3 or y=4/3
Putting in eqn 2
x=2 or x=9/2=4.5

Answer 2

Hey !!

2x + 3y = 13

xy = 6

[2x + 3y]³ = 13³

[2x]³ + [3y]³ + 3 × [2x]² × 3y + 3 × 2x × [3y]²  = 2197

8x³ + 27 y³ +  36x²y + 54xy² = 2197 

8x³ + 27 y³ + 18 xy [ 2x + 3y ] = 2197

4x³ + 27 y³ + 18 × 6 × 13 = 2197

8x³ + 27 y³ + 1404 = 2197

8x³ + 27 y³ = 2197 - 1404

8x³ + 27 y³  =  793

Hope this Helps You !!