       Re: New user with a problem, Can anyone help?

• To: mathgroup at smc.vnet.net
• Subject: [mg33208] Re: [mg33191] New user with a problem, Can anyone help?
• From: BobHanlon at aol.com
• Date: Sat, 9 Mar 2002 03:19:23 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 3/7/02 3:18:13 AM, royjmckee at aol.com writes:

>Currently doing a homework exercise and stuck on a question.
>
>Question:
>Find all values of x and y for which both
>409 - 166x + 17x^2 - 218y + 92xy - 10x^2 y + 34y^2 - 16xy^2 + 2x^2 y^2
>
>and
>23 - 5x - 8y + 2
>are equal to zero.
>
>Hence find expressions a and b (involving x and y) such that these two
>expressions are equal to a^2 + b^2 and a + b, respectively.
>
>Can anyone help or give any hints as I am struggling to grasp this question?
>

Use explicit multiplication to avoid writing xy when you mean x*y.

Your second expression has two constant terms (23+ ... +2).  Should one of
these involve a variable?

Solve[{409-166*x+17*x^2-218*y+92*x*y-10*x^2*y+34*y^2-16*x*y^2+2*x^2*y^2==0,
23-5*x-8*y+2==0},
{x,y}]//Simplify

Solve[{409-166*x+17*x^2-218*y+92*x*y-10*x^2*y+34*y^2-16*x*y^2+2*x^2*y^2==
a^2+b^2,
23-5*x-8*y+2==a+b},
{a,b}]//Simplify

Bob Hanlon
Chantilly, VA  USA

```

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