Hello!
Please help me to solve this inequality!
p(x^2+2)<2x^2+6x+1, if p is parameter!
Do you know the quadratic formula?
When you have $\displaystyle ax^2+bx+c=0,x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} $
In your case.
$\displaystyle p(x^2+2)<2x^2+6x+1$
$\displaystyle px^2+2p<2x^2+6x+1$
$\displaystyle 0<2x^2-px^2+6x+1-2p$
$\displaystyle 2x^2-px^2+6x+1-2p<0$
$\displaystyle (2-p)x^2+6x+1-2p<0$
Now use $\displaystyle a = 2-p, b=6, c = 1-2p$ into the quadratic formula