Question

if a minus b equal to 7 and a cube minus b cube is equals to 13 3 find a b​

Answer 1

Given

• a - b = 7
• a - b = 7 a³ - b³ = 133

To Find :

• Value of a and b

Solution :

⇰ a - b = 7

⇰ a = 7 + b ...... 1

a³ - b³ = 133

Put value of a from 1

⇰ ( 7 + b )³ - b³ = 133

⇰ 343 + 147b + 21b² + b³ - b³ = 133

⇰ 21b² + 147b + 210 = 0

⇰ b² + 7b + 10 = 0

By splitting middle term

⇰ b² + 5b + 2b + 10 = 0

⇰ b ( b + 5 ) 2 ( b + 5 ) = 0

⇰ ( b + 5 ) ( b + 2 ) = 0

⇰ b = - 5

⇰ b = - 2

Here b have two values. Put these in 1 to find a

1st vaue

⇰ a = 7 + ( - 5 )

⇰ a = 2

2nd value

⇰ a = 7 + ( - 2 )

⇰ a = 5

Value of a = 2 , 5 and b = -2 , - 5