Question

If x − y = 5 and xy = 84, find the value of x 3 – y 3 .

Answer 1

Step-by-step explanation:

x - y = 5

xy = 34.

(x−y)

2

=x

2

+y

2

−2xy=25

x

2

+y

2

−2×84=25

x

2

+y

2

=193

also, (x+y)

2

=x

2

+y

2

+2xy

=193+84×2

= 361

x+y=

361

=14

solution

Answer 2

Step-by-step explanation:

x-y=5

xy=84 .....1

x-y=5

x=5+y …2

substitute the value of equation 1 into equation 2

xy=84

(5+y)y=84

5y+y square =84

y square +5y-84=0

y square +12y-7y-84 =0

y(y+12) -7(y+12) =0

(y-7) or (y+12) =0

y=7 or y =-12

x-y =5

x-(7)=5. ; x-(-12)=5

x=5+7 x+12=5

x=12 x=5-12

x=-7

x=12 or x=-7

suppose ,

x=12 and y =7

3x-3y

=3(12)-3(7)

=36-21

=15