Question 201065
[(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




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