Question

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

Answer 1

Answer:

Yes, that is correct.

Step-by-step explanation:

a would always have to be greater than b since you're just multiplying each variable by itself.

Answer 2

Answer:

Yes

Step-by-step explanation:

$a^2>b^2$ means $a^2-b^2>0$.

Factoring the left hand side gives me:

$(a-b)(a+b)>0$

Since $a,b$ are positive then $a+b$ is positive so dividing both sides by this will not effect the direction of the inequality:

$a-b>0$

Adding $b$ on both sides gives:

$a>b$