Question

if x-y=2 and xy=15 find the x^3-y^3​

Answer 1

Answer:

116 or 56

Step-by-step explanation:

x-y =2

or

x= y+2

substitute this in xy = 15

(y+2)y =15

y^2 + 2y = 15

y^2 + 2y - 15 = 0

solving quadratic eqn

y^2 - 3y + 5y -15 = 0

y = -5 y = 3

x - y = 2

when y = 3 ,x = 5

when y= 2, x = 4

so x^3 - y^3 = 5^3 - 3^3 = 125 - 9 = 116

or

4^3 - 2^3 = 64 - 8 = 56

so ans is 116 or 56

Answer 2

Hey there!!

We have two values already :

x - y = 2

xy = 15

We will need to find x³ - y³

Let's cube the first equation on both sides:

... ( x - y )³ = ( 2 )³

... x³ - 3xy( x - y ) - y³ = 8

... We know xy is 15, then 3xy would be 45 and x - y is 2

... x³ - 45( 2 ) - y³ = 8

... x³ - 90 - y³ = 8

... x³ - y³ =  98

The answer is 98.