Question

if the value of (a+b)and ab are 12 and 32 respectively, find the value of a^2+b^2and (a-b) ^2.​

Answer 1

Answer:

a² + b² = 80 , ( a - b )² = 16

Step-by-step explanation:

Given ---> a + b = 12 and ab = 32

To find ---> a² + b² = ? , (a - b )² = ?

Solution---> We have two identities

(1) ( a + b )² = a² + b² + 2ab

(2) ( a - b )² = a² + b² - 2ab

ATQ,

a + b = 12

Squaring both sides

( a + b )² = ( 12 )²

=> a² + b² + 2ab = 144

=> a² + b² = 144 - 2ab

=> a² + b² = 144 - 2 ( 32 )

=> a² + b² = 144 - 64

=> a² + b² = 80

Now

(a - b )² = a² + b² - 2ab

= ( a² + b² ) - 2 ( ab )

= ( 80 ) - 2 ( 32 )

= 80 - 64

( a - b )² = 16