Question

I Need this answered asap thanks for helping ​

Answer 1

y = 3 or y = 7

Explanation:

`\bold{METHOD\ 1}\\(y-3)^2=4y-12\\\\(y-3)^2=4(y-3)\\\\(y-3)(y-3)=4(y-3)\iff y-3=0\ \vee\ y-3=4\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}\\\\y-3=4\qquad\text{add 3 to both sides}\\\boxed{y=7}`

`\bold{METHOD\ 2}\\\\(y-3)^2=4y-12\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\y^2-2(y)(3)+3^2=4y-12\\\\y^2-6y+9=4y-12\qquad\text{subtract}\ 4y\ \text{from both sides}\\\\y^2-10y+9=-12\qquad\text{add 12 to both sides}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0\\\\(y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}\\\\y-7=0\qquad\text{add 7 to both sides}\\\boxed{y=7}`