Math Question

[MrCodeDude]

x^2 + x + y^2 + y = 50, x + y = 8. Find xy.

So you get:
x^2 + y^2 = 42
y^2 = 42 - x^2
y = sqrt [42-x^2]
0 = sqrt [42-x^2]
x = 6.48

x + y = 8, so y = 1.52

But going back to the original equation, it comes out to 52 and change?

Help?

 

[UncleWai]

Substitute all Y with (8-x)

so you have x^2 + x + (8-x)^2 + (8-x) = 50

 

[BigJ]

Solve for either x or y using the 2nd equation and subsitute.

 

[MrCodeDude]

Oh snap, I'm stupid. Calculus had mudded my knowledge with trig deriv and integral memorizingnes..

 

[DrPizza]

There's a quicker solution.

x+y = 8
square both sides
x^2 +2xy + y^2 = 8
x^2 + y^2 = 8 - 2xy

Substitute into the first equation
x^2 + y^2 = 42
8 - 2xy = 42
and solve for xy.

 

[BigPoppa]

Originally posted by: DrPizza
There's a quicker solution.

x+y = 8
square both sides
x^2 +2xy + y^2 = 64?
x^2 + y^2 = 64? - 2xy

 

[oboeguy]

Originally posted by: BigPoppa

Originally posted by: DrPizza
There's a quicker solution.

x+y = 8
square both sides
x^2 +2xy + y^2 = 64?
x^2 + y^2 = 64? - 2xy

That would have been my solution as well. Elegant. And yes, 8^2 = 64, for typical values of 8.

 

[Yossarian]

"x^2 + x + y^2 + y = 50"

I copyrighted that equation in the 9th grade, I can't believe you didn't give me credit for it.

 

[MrCodeDude]

Originally posted by: Yossarian
"x^2 + x + y^2 + y = 50"

I copyrighted that equation in the 9th grade, I can't believe you didn't give me credit for it.

Then you should call up CollegeBoard and ask them why it was on the November SAT.

 

[Muzzan]

*edit* Sigh, why didn't I bother to read the entire thread before posting?

 

[chuckywang]

xy = 11

 

[Evadman]

2 + 2 is 5 for moderately large values of 2.

 

[chuckywang]

Originally posted by: Evadman
2 + 2 is 5 for moderately large values of 2.

says the physicist?

 

[DrPizza]

Originally posted by: BigPoppa

Originally posted by: DrPizza
There's a quicker solution.

x+y = 8
square both sides
x^2 +2xy + y^2 = 64?
x^2 + y^2 = 64? - 2xy

oh geeeezzzz.. Thanks. Hey, I had it right on the back of an envelope when I jotted it down just to make sure... I just wasn't paying close enough attention when I was typing it.