I am given a utility function $u(x)=x_1^2+x_2^2$ and I am asked to see whether this function satisfies strict convexity. The answer is saying this:

We see that $u(3,0) = 9$, $u(0,3) = 9$, $u(1.5,1.5) = 4.5$. Here, $x = (3,0)$, $y = (0,3)$, and $z = (3,0)$, we have $x ≳ z$ and $y ≳ z$, but $tx + (1 − t)y ≺ z$ for $t=1/2$.

I am lost at this part here $tx + (1 − t)y ≺ z$ for $t=1/2$; isn't the utility still 9, which is the same as the utility of every bundle there?


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