Question

Find the two positive numbers whose sum is 15 and sum of whose squares is minimum

Answer 1

Step-by-step explanation:

a+b=15

f(a,b)=a

2

+b

2

is minimum

f(a)=a

2

+(15−a)

2

f

′

(a)=2a−2(15−a)=4a−30=0

a=

2

15

,b=

2

15

So a=

2

15

,

2

15

are two numbers for which f(a,b)=a

2

+b

2

is minimum

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Answer 2

a+b=15

f(a,b)=a

2

+b

2

is minimum

f(a)=a

2

+(15−a)

2

f

′

(a)=2a−2(15−a)=4a−30=0

a=

2

15

,b=

2

15

So a=

2

15

,

2

15

are two numbers for which f(a,b)=a

2

+b

2

is minimum

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