<s>[INST] What is the smallest value of $x^2+y^2$ when $x+y=6$? If $ x+y=6 $ then what is the smallest possible value for $x^2+y^2$?
Please show me the working to show where I am going wrong!
Cheers
 [/INST] $$x^2+y^2\geq 2xy\implies 2(x^2+y^2)\geq (x+y)^2$$
Hence, $$(x^2+y^2)\geq \frac{6^2}{2}=18$$
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