Is the following true for all positive values of a and b: if a> b then a^2> b^2

Yes

Step-by-step explanation:

If , then .

If are positive, then .

So if I multiply both sides of by it will not effect the direction of the inequality since it is of positive value.

This actions gives us .

Using foil we can multiply the left hand side out resulting in:

Add on both sides:

.

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Also consider the function .  This function increases after is 0.  This means as you increase the value for the value for increases for positive value inputs of .