Question

Please help me with 6th question

Answer 1

Here is your answer :

a - b = 7

a = 7 + b

( 7 + b ) × b = 18

7b + b^2 = 18

b^2 + 7b - 18 = 0

b^2 + 9b - 2b - 18 = 0

b ( b + 9 ) - 2 ( b + 9 ) = 0

( b - 2 ) ( b + 9 ) = 0

b = 2

a = 7 + b

a = 7 + 2

a = 9

So a + b = 9 + 2 = 11

Hope it helps you.

Answer 2

Given a - b = 7 and ab = 18.

On squaring both sides, we get

= > (a - b)^2 = (7)^2

= > a^2 + b^2 - 2ab = 49

= > a^2 + b^2 - 2(18) = 49

= > a^2 + b^2 - 36 = 49

= > a^2 + b^2 = 49 + 36

= > a^2 + b^2 = 85.

We know that a^2 + b^2 = (a + b)^2 - 2ab

= > 85 = (a + b)^2 - 2(18)

= > 85 = (a + b)^2 - 36

= > 85 + 36 = (a + b)^2

= > 121 = (a + b)^2

= > a + b = 11.


Therefore the value of a + b = 11.


Hope this helps!