Find two numbers whose sum is 10 and the sum of whose squares is minimum.
Find two numbers whose sum is 10 and the sum of whose squares is minimum.
Let x and y be the numbers.
x+y=10
y=10-x
Let S be the sum.
S= x2 + y2
S= x2 + (10-x)2
dS/dx = 2x+2(10-x) *(-1)
dS/dx = 2x-20-2x
dS/dx = 4x-20
d2S/dx2 = 4>0 (Minimum)
dS/dx =0
4x-20=0
4x=0
x=5
y=10-x = 10-5 =5
Hence the two numbers are 5 and 5