G9.2 If the expression $\left(x^{2}+y^{2}\right)^{2} \leq b\left(x^{4}+y^{4}\right)$ holds for all real values of $x$ and $y$, find the least possible integral value of $b$.
$$
b\left(x^{4}+y^{4}\right)-\left(x^{2}+y^{2}\right)^{2}=b\left(x^{4}+y^{4}\right)-\left(x^{4}+y^{4}+2 x^{2} y^{2}\right)=(b-1) x^{4}-2 x^{2} y^{2}+(b-1) y^{4}
$$

If $b=1$, the expression $=-2 x^{2} y^{2}$ which cannot be positive for all values of $x$ and $y$.
If $b \neq 1$, discriminant $=(-2)^{2}-4(b-1)^{2}=4\left(1-b^{2}+2 b-1\right)=-4 b(b-2)$
In order that the expression is always non-negative, $(b-1)>0$ and discriminant $\leq 0$
$b>1$ and $-4 b(b-2) \leq 0$
$b>1$ and $(b \leq 0$ or $b \geq 2$ )
$\therefore b \geq 2$, the least possible integral value of $b$ is 2 .