You need to remember that `(sqrtx - sqrty)^2 gt=0 =gt x - 2sqrt(xy) + y gt= 0 =gt x + y gt 2sqrt(xy)` .

`(sqrty - sqrtz)^2 gt= 0 =gt y+ z gt= 2sqrt(yz)`

`(sqrtz - sqrtx)^2 gt= 0 =gt z+x gt= 2sqrt(zx)`

Multiplying the inequalities yields:

`(x+y)(y+z)(z+x)gt=(2sqrt(xy))*(2sqrt(yz))*(2sqrt(zx))`

`(x+y)(y+z)(z+x)gt=8(sqrt(x^2*y^2*z^2))`

Since x,y,z are positive numbers => `(sqrt(x^2*y^2*z^2)) = xyz`

(x+y)(y+z)(z+x)`gt=` 8xyz

**Hence, the last line proves that the inequality is checked.**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now