SOLUTION: For what value(s) of the coefficient a do the equations x^2-ax + 1=0 and x^2-x+a=0 have a common real solution?

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Question 76463: For what value(s) of the coefficient a do the equations x^2-ax + 1=0 and x^2-x+a=0 have a common real solution?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For what value(s) of the coefficient a do the equations x^2-ax + 1=0 and x^2-x+a=0 have a common real solution?
:
x^2 - ax + 1 = x^2 - x + a
:
x^2 - x^2 - ax - a = -x - 1
:
-ax - a = -x - 1; x^2's eliminated
:
ax + a = x + 1; multiplied by -1 to get rid of all those negatives
:
a(x+1) = x+1; factor out a
:
a = (x+1)/(x+1); divide both sides by (x+1)
:
a = 1; the common real solution