Question

If x-y = 4 and xy = 21 then find the value of x 3 - y 3

Answer 1

x-y=4----(1)

xy=21----(2)

square both sides of (1)

(x-y)²=x²+y²-2xy
4²=x²+y²-2*21 [ from (1) and (2)]

16= x²+y²-42

16+42 =x²+y²
x²+y²=58---(3)

x³-y³ = (x-y)( x2+y²+xy)

= 4*(58+21)
=4*79
=316

Answer 2

Answer:

x³ - y³ = 316

Step-by-step explanation:

$x - y = 4 \\ xy = 21 \\ {x}^{3} - {y}^{3} = \: \: ?? \\ \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) \\ {4}^{3} = {x}^{3} - {y}^{3} - 3(21)(4) \\ 64 = {x}^{3} - {y}^{3} - (63 \times 4) \\ 64 = {x}^{3} - {y}^{3} - 252 \\ 64 + 252 = {x}^{3} - {y}^{3} \\ \underline{ \underline{ 316}} = {x}^{3} - {y}^{3}$