Question

if 2x-3y=10 and xy=16 find the value of 8x cube-27y cube

Answer 1

Hii friend,

2X-3Y = 10........(1)

XY = 16.....(2)

2X -3Y = 10

2X = 10+3Y

X = 10+3Y/2......(3)

Putting the value of X in equation (2)

XY = 16

(10+3Y/2) × Y = 16

Y(10+3Y) = 32

10Y + 3Y² = 32

3Y²+10Y -32 = 0

3Y² - 6Y + 16Y - 32 = 0

3Y(Y-2) + 16(Y -2)

(Y-2) ( 3Y+16)

Y -2 = 0. or 3Y +16 = 0

Y = 2. or 3Y = -16

Y = 2. or Y = -16/3

X = 10+3Y/2 = 10+ 3 × 2/2 = 13

THEREFORE,

8X³ - 27Y =

8 × (13)³ - 27 × 2

8 × 39 - 54 = 312 - 39 = 273


HOPE IT WILL HELP YOU..... :-)