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Grade: 12
        
show that among all positive numbers x and y with x^2 + y^2 = r^2, the sum of x+y is largest when x=y=r/(sqrt 2)
3 years ago

Answers : (2)

Arun Kumar
IIT Delhi
askIITians Faculty
256 Points
							Hi

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
3 years ago
Rinkoo Gupta
askIITians Faculty
80 Points
							

S=x+y=x+v(r2-x2)

Ds/dx=1+(-2x)/2v(r2-x2) put ds/sx=0 , we get

1-x/v(r2-x2)=0

ð X=r/v2

ð D2s/dx2=0- { v(r2-x2).1+x2/v(r2-x2)}

ð D2/dx2=-r2/v(r2-x2)

Pur x=r/v2, we get

Y=v(r2-x2)

=v(r2-r2/2

=vr2/2

=r/v2

So x=y=r/v2

Thanks & regards

Rinkoo Gupta

askIITians faculty

3 years ago
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