Question

If a-b = 7 and ab = 8. Find the value of a^3 - b^3 (a cube - b cube)​

Answer 1

Answer:

511

Step-by-step explanation:

a-b = 7 ____eq 1

ab = 8 ____eq 2

a = 7 + b ___eq 3

a = 8/b ___eq 4

using simultaneous equations :

7 + b = 8/b

7b + b^2=8

b^2 + 7b - 8 =0

factorize it

b^2 + 8b - b - 8 = 0

b(b+8) -1(b+8)=0

b = 1 , -8

then a = 8/1 = 8

a =8/-8 = -1

a = 8, -1

so,

a^3 - b^3

= (8)^3-(1)^3

= 511