Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 29, 2011"
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− | First we have the question: (ab+1)(a+1)(b+1)+ab | + | First we have the question: <math>(ab+1)(a+1)(b+1)+ab<math> |
− | We multiply (a+1)(b+1) to get (ab+1+a+b) | + | We multiply <math>(a+1)(b+1)<math> to get <math>(ab+1+a+b)<math> |
− | This makes the equation (ab+1)(ab+1+a+b)+ab | + | This makes the equation <math>(ab+1)(ab+1+a+b)+ab<math> |
Now we seperate the equation to <math>(ab+1)(ab+1)+(ab+1)(a+b)+ab</math> | Now we seperate the equation to <math>(ab+1)(ab+1)+(ab+1)(a+b)+ab</math> | ||
− | We get (ab+1)^2 +(a+b)(ab+1)+ab | + | We get <math>(ab+1)^2 +(a+b)(ab+1)+ab<math> |
Now this is just a quadratic equation | Now this is just a quadratic equation |
Revision as of 23:09, 28 June 2011
Problem
AoPSWiki:Problem of the Day/June 29, 2011
Solution
This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it.
First we have the question: $(ab+1)(a+1)(b+1)+ab<math>
We multiply <math>(a+1)(b+1)<math> to get <math>(ab+1+a+b)<math>
This makes the equation <math>(ab+1)(ab+1+a+b)+ab<math>
Now we seperate the equation to <math>(ab+1)(ab+1)+(ab+1)(a+b)+ab$ (Error compiling LaTeX. Unknown error_msg)
We get $(ab+1)^2 +(a+b)(ab+1)+ab<math>
Now this is just a quadratic equation
Thus we get a factored form of:
<math>(ab+1+a)(ab+1+b)$ (Error compiling LaTeX. Unknown error_msg)
That is the solution