Solve these questions, If you can........

1). Determine the number of ordered triples of positive integers (a,b,c) such that a+b+c+ab+bc+ac=abc+1.

2). How many ordered sets of integers (x,y,z) such that x,y, and z are between −10 and 10 inclusive are solutions to the following system of equations:

x^2y^2+y^2z^2=5xyz, y^2z^2+z^2x^2=17xyz, z^2x^2+x^2y^2=20xyz?

Easy Math Editor

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`bold` or `__bold__`	bold
- bulleted - list	bulleted list
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

These are live problems!

Vikram Waradpande - 7 years, 8 months ago

You may join the solution discussion to see how others approached the problem.

This discussion will be locked.

Calvin Lin Staff - 7 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$