Question

If a-b=4 and ab=21 find the value of a cube- b cube

Answer 1

a^3 - b^3 =(a-b)^3 +3ab(a-b)
=(4)^3 +3.21(4) [by putting the value]
=64+252
=316

Answer 2

a - b = 4
ab = 21
a^3 - b^3 = ?
a - b = 4
a = b + 4.......(1)
By substituting the value of 'a' in the equation ab = 21
(b + 4) (b) = 21
b^2 + 4b = 21
b^2 + 4b - 21 = 0
b ^2 +7b - 3b -21 = 0
b (b + 7) -3 ( b + 7)
(b+7) (b-3)
So the value of 'b' can be -7 or 3
If b= -7 , then a - b= 4
a - (-7) = 4
a+7 = 4
a= -3
Now , a^3 - b3 = (-3)^3 - (-7)^3
= -27 - ( -343)
= -27 + 343
= 316