Question

A^2+b^2=10 if ab=4 then find the value of 3(a+b)^2-2(a-b) ^2

Answer 1

Answer:

50

Step-by-step explanation:

Given----> a² + b² = 10 and ab = 4

To find------> 3 ( a + b )² - 2 ( a - b )²

Solution----> We know that,

( a + b )² = a² + b² + 2ab

= ( a² + b² ) + 2 ( ab )

Putting, ( a² + b² ) = 10 and ab = 4

( a + b )² = ( 10 ) + 2 ( 4 )

= 10 + 8

= 18

Now, we know that,

( a - b )² = a² + b² - 2ab

= ( a² + b² ) - 2 ( ab )

= ( 10 ) - 2 ( 4 )

( a - b )² = 10 - 8

( a - b )² = 2

Now,

3 ( a + b )² - 2 ( a - b )² = 3 ( 18 ) - 2 ( 2 )

= 54 - 4

= 50