Question

Question #f41ff

Answer 1

`A+B=40`

Explanation:

If `9` is a solution to the equation `x^2-4x=A` then:

`A = color(blue)(9)^2-4(color(blue)(9)) = 81-36 = 45`

So `B` is the other solution to:

`x^2-4x=45`

Add `4` to both sides to get:

`x^2-4x+4 = 49`

That is:

`(x-2)^2 = 7^2`

Hence:

`x-2 = +-7`

Add `2` to both sides to get:

`x = 2+-7`

That is:

`x = 9" "` or `" "x = -5`

So `B=-5`

So `A+B = 45+(-5) = 40`

Answer 2

`A+B+40.`

Explanation:

By what is given, `B and 9` are the roots of the Quadr. Eqn.,

`x^2-4x-A=0.`

Knowing that, in the Quadr. Eqn. `:ax^2+bx+c=0,`

Sum of Roots `=-b/a," and, Product of Roots ="c/a`, we have,

`B+9=-(-4)/1=4 rArr B=-5, &, 9B=-A/1=-A, or, A=-9B`

Hence, `A+B=-9B+B=-8B=(-8)(-5)=40,` as Respected George C. Sir has already derived!

Enjoy Maths.!