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

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Lesson Parent:

Problem:

Answer:

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

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

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

$x_2$ to get

Since