<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] When Usually found yourself stuck at such questions:
One can Go for Hit and Trial Method:
Since the value of 
 x+y = 6
Start with lowest possible combination you can think of
For x=1, y=5 : $x^2+y^2=26$
For x=2, y=4 : $x^2+y^2=20$
For x=3, y=3 : $x^2+y^2=18$
For x=4, y=2 : $x^2+y^2=20$
For x=5, y=1 : $x^2+y^2=26$
So the minimum is 18
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