Prove that if $0\lt x_1\lt x_2$, then $x^2_1\lt x^2_2$.

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Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if $0\lt x_1\lt x_2$, then $x^2_1\lt x^2_2$.

Answer: 

It is true that if $0\lt x_1\lt x_2$, then $x^2_1\lt x^2_2$.

SAMPLE SOLUTION

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Solution: 

Since $x_1$ and $x_2$ are both greater than zero then we can multiply <Sign in to see all the formulas> by either one of them and not change $\lt$ to $\gt$. Therefore, we can multiply both sides of <Sign in to see all the formulas> by $x_1$ to get

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We can also multiply both sides of <Sign in to see all the formulas> by $x_2$ to get

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Since

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our Rules of Inequalities tell us that

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