Question

If 2a2 – 2ab + b2 + 6a + 9 = 0, then (a + b) + ab equals?​

Answer 1

Step-by-step explanation:

Please find below the solution to the asked query:

We have : 2 a2 - 2 ab + b2 + 6 a + 9 = 0 , So

⇒ a2 - 2 ab + b2 + a2 + 6 a + 9 = 0

⇒( a2 - 2 ab + b2 ) + ( a2 + 2 ( a ) ( 3 ) + 32 )= 0

⇒( a - b )2 + ( a + 3 )2 = 0

We know sum of any two square term only be equal to zero if all terms ( here both terms ) are equal to zero , So

( a - b )2 = 0

a - b = 0

a = b --- ( 1 )

And

( a + 3 )2 = 0 ,

a + 3 = 0

a = - 3 , From equation 1 we get

a = b = - 3

So ,

Values of ( a + b ) + a b we get by substituting values of ' a ' and ' b ' .

⇒ ( - 3 + ( - 3 ) ) + ( - 3 ) ( - 3 )

⇒ ( - 3 - 3 ) + 9

⇒ - 6 + 9

⇒ 3 ( Ans )

Hope this information will clear your doubts about topic.