Solve Algebra: 16+(y-6)^2=9+(y-5)^2

[DB]

When

\sqrt{16 + (y-6)^2}=\sqrt{9+(y-5)^2}

is simplified to:

16+(y-6)^2=9+(y-5)^2

How come the 16 and 9 arent square rooted?

Thanks

 

[Muzza]

Do you agree that \sqrt{a} = \sqrt{b} implies a = b?

If so, what happens when you set a = 16 + (y - 6)^2 and b = 9 + (y - 5)^2?

 

[DB]

ahhh, o you its because they are equal, i got mixed up thanks.
But \sqrt{16 + (y-6)^2}
doesn't simplify to 16+(y-6)^2 right?

 

[Muzza]

Correct. It would have if the expression was \sqrt{ (16 + (y - 6)^2)^2 } though ;)

 

[DB]

ya thanks muzza

 

[HallsofIvy]

If you square both sides of the equation,
\sqrt{16- (y-6)^2}= \sqrt{9- (y-5)^2}
you eliminate the two square roots and you get
16- (y-6)²= 9- (y-5)².