Question

if a-b=7and a^2+b^2=85finda^3_b^3​

Answer 1

Answer:

721

Step-by-step explanation:

Given-----> a - b = 7 and a² + b² = 85

To find ----> a³ + b³ = ?

Solution----> We know that,

( a - b )² = a² + b² - 2ab

Putting a - b = 7 and a² + b² = 85 , we get,

=> ( 7 )² = ( 85 ) - 2ab

=> 49 = 85 - 2ab

=> 2ab = 85 - 49

=> 2ab = 36

=> ab = 18

Now , we know that,

( a³ - b³ ) = ( a - b ) ( a² + b² + ab )

= ( a - b ) { ( a² + b² ) + ab }

= ( 7 ) { ( 85 ) + 18 }

= ( 7 ) ( 103 )

=> ( a³ - b³ ) = 721