Understanding Inequalities: Part II Question | Need Help?

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I need help with the second part, I've managed to get through all of the part (i), but I have no idea where to really start with part (ii), any hints to start me off and I'll keep posting how I'm doing.

thanks
 
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hi synkk! :smile:

(i don't know whether this works :redface:, but …)

i'd try rewriting it as a + b + c ≥ 3abc :wink:
 
Hint: the last equality can be rewritten as:
\frac{trs^2 + rst^2+ tsr^2}{rst}
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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