Solve the quadratic equation by completing.
[math]y ^ { 2 } - 6 y + 9 = 0[/math]
I am asking this question because if you solve this problem by factorization method, you get y = 3 twice.
My concern here is why am I getting y = 3 only once instead of twice.
[math]y ^ { 2 } - 6 y + 9 = 0[/math]
Solution
[math]y ^ { 2 } - 6 y = -9[/math][math]y ^ { 2 } - 6 y +\left(\frac{1}{2}×(-6)\right) ^2= -9+\left(\frac{1}{2}×(-6)\right) ^2[/math][math]y ^ { 2 } - 6+9 y = -9+9[/math][math]y ^ { 2 } - 6 y +9 = 0[/math][math]\left(y-3\right)^2=0[/math][math]y-3 = \pm\sqrt{0}[/math][math]y-3=0[/math][math]\therefore ~ y=3[/math]Is y really 3?I am asking this question because if you solve this problem by factorization method, you get y = 3 twice.
My concern here is why am I getting y = 3 only once instead of twice.
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