# precise evaluation – On some inequality (higher certain) on an obligation of two variables retort

Hello pricey customer to our community We will proffer you an answer to this query precise evaluation – On some inequality (higher certain) on an obligation of two variables ,and the retort will breathe typical by means of documented info sources, We welcome you and proffer you contemporary questions and solutions, Many customer are questioning in regards to the retort to this query.

## precise evaluation – On some inequality (higher certain) on an obligation of two variables

There is an issue (of somatic inception) which wants an analytical answer or a confidential. Let us assume the next actual-valued responsibility of two variables

$$y (t,a) = 4 left(1 + frac{t}{x(t,a)}capable)^{ – a – 1/2} left(1 – frac{2}{x(t,a)}capable)^{ 1/2} (x(t,a))^{-3/2} (z(t,a))^{1/4} left(1 + frac{t}{2}capable)^{ a},$$

the place $$t > 0$$, $$0 < a < 1$$ and

$$x(t,a) = frac{a-1}{2} t + frac{3}{2}+frac{1}{2}sqrt{z(t,a)}$$,

$$z(t,a) = (1-a)^2 t^2+ 2(3-a)t +9.$$

It is needful to show that

$$y(t,a) < 1$$

for all $$t > 0$$ and $$0 < a < 1$$. The numerical evaluation helps this certain.

P.S. I apologize for too “technical” query. It appears that the inequality is precise too for $$a = 1$$
however it fails for $$a > 1$$.

we’ll proffer you the answer to precise evaluation – On some inequality (higher certain) on an obligation of two variables query by way of our community which brings all of the solutions from a number of reliable sources.