Question

if a^2+b^2=25 and ab=12 find 3(a+b)^2-5(a-b)^2​

Answer 1

Answer:

142

Step-by-step explanation:

a² + b² = 25

Adding 2ab on both sides

⇒ a² + b² + 2ab = 25 + 2ab

⇒ ( a + b )² = 25 + 2( 12 )

⇒ ( a + b )² = 25 + 24

⇒ ( a + b )² = 49

Using algebraic identity

( a - b )² = ( a + b )² - 4ab

⇒ ( a - b )² = 49 - 4( 12 )

⇒ ( a - b )² = 49 - 48

⇒ ( a - b )² = 1

Now, 3( a + b )² - 5( a - b )²

= 3( 49 ) - 5( 1 )

= 147 - 5

= 142