SOLUTION: Find the values of a and b that result in the given sum. [(a+1)x^2 + bx + 2] + [(b-2)x^2 - ax + 5] = x^2

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Question 201065: Find the values of a and b that result in the given sum.
[(a+1)x^2 + bx + 2] + [(b-2)x^2 - ax + 5] = x^2 - 4x + 7

Please help. Thanks
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
[(a+1)x^2 + bx + 2] + [(b-2)x^2 - ax + 5] = x^2 - 4x + 7 ... Start with the given equation.

(a+1)x^2 + bx + 2 + (b-2)x^2 - ax + 5 = x^2 - 4x + 7 ... Remove the brackets

[(a+1)x^2+ (b-2)x^2] + [ bx - ax] + [2 + 5] = x^2 - 4x + 7 ... Group like terms.

(a+1+b-2)x^2 + (b-a)x + 7 = x^2 - 4x + 7 ... Combine like terms.

(a+b-1)x^2 + (b-a)x + 7 = x^2 - 4x + 7 ... Simplify

Now just equate the coefficients to get the two equations:

a+b-1=1
b-a=-4

So simply solve this system (which I'll let you do) using any method to get the answers
a=3, b=-1

If you have any questions, email me at jim_thompson5910@hotmail.com.
Check out my website if you are interested in tutoring.

SOLUTION: Find the values of a and b that result in the given sum. [(a+1)x^2 + bx + 2] + [(b-2)x^2 - ax + 5] = x^2 - 4x + 7 Please help. Thanks