Question #f41ff

2 Answers
Mar 12, 2017

Answer:

#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#

Mar 14, 2017

Answer:

#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.!