The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squar

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The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?
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you have every calculus question that my teacher gives! I appreciate your help

thetvchannel
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The sum of two no.is 17, whereas sum of their squares is 145.what is the product of 2 no.? Sir plz solve this question

preetikamal
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sum of a number and its reciprocal is 4 then value of sum of the number and reciprocal of the cube is ?

ThiraiMeelar
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Can be done in a simple way
x+y=16
s=x^2 + (16-x)^2
now put x=7 we get 49+ 81=130 same way for x=9 we again get 130
now therefore we got back to same value therefore there must be critical value at middle which is for x=8..
for x=8 we get 128

kunalchhetri