Question

solve for y:(y-13)^2+(y+13)^2=4712. Please show me how do it step by step.

Answer 1

Because of the pattern of the problem, the middle terms will cancel one another when expanded so\[2y ^{2}+338=4712\]

Answer 2

After a little rearrangement and simplification,
\[y ^{2}-2187=0\]

Answer 3

First, you need to expand the equation, so \[(y-13)^2 + (y+13)^2 = y^2-26y+169 +y^2+26y+169=4712\]Thus, by combining like terms,\[2y^2+338=4712\] From here, subtract 4712 to get\[2y^2-4374=0\]Divide by 2,\[y^2-2187=0\] and factor.\[(y-\sqrt{2187})(y+\sqrt{2187})=0\]

Answer 4

Nice work KG, you clearly type faster than I do....LOL

Answer 5

Merely more familiar with \( \LaTeX\)

Answer 6

Thanks! the answer is is plus or minus 27sqrt3.how do i get it

Answer 7

2187 is 3^7, then take the square root.

Answer 8

Since \[(y-\sqrt{2187})(y+\sqrt{2187}) =0\]Either \(y=\sqrt{2187}\) or \(y=-\sqrt{2187}\) So \(y=\pm \sqrt{2187}\) Since \(\sqrt{2187}=3\sqrt{27}\),
\(y=\pm 3\sqrt{2187}\)

Answer 9

I got it.Thanks for the help!

Answer 10

You're welcome.