Posted by **Lily** on Friday, May 17, 2013 at 10:06am.

Find the exact solutions of x^2 - (y - 6)^2 = 36 and y = -x^2.

(0,0), (6,6), and (-6,6)?

- Algebra 2 -
**Steve**, Friday, May 17, 2013 at 10:30am
Hmmm.

y = -x^2 so

x^2 - (-x^2-6)^2 = 36

x^2 - x^4 - 12x^2 - 36 = 36

x^4 + 11x^2 + 72 = 0

I don't see any real solutions. 11^2-4*72 < 0

- Algebra 2 -
**Lily**, Friday, May 17, 2013 at 10:42am
Thanks

- Algebra 2 -
**Steve**, Friday, May 17, 2013 at 10:49am
And yet, I do see that your points work.

Hmmm.

- Algebra 2 -
**Steve**, Friday, May 17, 2013 at 10:53am
No, they don't they fit the first equation, but not the 2nd.

Only (0,0) works in both

- Algebra 2 -
**Steve**, Friday, May 17, 2013 at 10:55am
Nope. (0,0) does not work in the 1st.

0 - 36 ≠ 36

Can't believe I let you fool me! :-)

- Algebra 2 -
**Lily**, Friday, May 17, 2013 at 11:24am
At this point, I'm fooling myself!:-)

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