Prove (x^2)+1/(x^2 )≥x + (1/x )≥2 for x> 0

First of all, let's prove that

We can rewrite the fraction as

And the inequality as

Again, we can rewrite as

The numerator is a square, so it is always greater than or equal to zero.

The denominator is positive, because we're assuming x>0.

So, this is a fraction between positive numbers, and it is always positive, and the first part is finished.

As for the second part, we have

The numerator is not the product of a square (always greater than or equal to zero) and a quadratic equation with no solutions and positive leading coefficient (always positive), so it's always greater than or equal to zero. The denominator is x^2, and since x>0 by hypothesis, it is positive. This ends the proof.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.