Question

2 X + Y = 12 x y = 210 find 8 x cube + y cube​

Answer 1

Correct Question :-

If 2x + y = 12, xy = 210, then find 8x³ + y³

Answer :-

8x³ + y³ = - 13392

Solution :-

2x + y = 12

Cubing on both sides

(2x + y)³ = 12³

(2x)³ + (y)³ + 3(2x)(y)(2x + y) = 1728

[ Because (a + b)³ = a³ + b³ + 3ab(a + b) and above a = 2x, b = y ]

8x³ + y³ + 6(xy)(2x + y) = 1728

8x³ + y³ + 6(210)(12) = 1728

[ Because xy = 210, 2x + y = 12 ]

8x³ + y³ + 72(210) = 1728

8x³ + y³ + 15120 = 1728

8x³ + y³ = 1728 - 15120

8x³ + y³ = - 13392

Identity used :-

• (a + b)³ = a³ + b³ + 3ab(a + b)