The sum of squares of two parts of a number 100 is minimum, then two parts are
Sum of square of two parts of a number 100,
Let, the required number are x and 100−x
Now, according to the question,
f(x)=x2+(100−x)2 ………(1)
Differentiate with respect to x,
f′(x)=2x+2(100−x)(−1) ……..(2)
For maxima and minima,
f′(x)=0
2x+2(100−x)(−1)=0
4x=200
x=50
Differentiate equation 2nd with respect to x,
f′′(x)=2−2(0−1)
f′′(x)=4
At x=50,
f′′(x)>0
Hence the function f(x)=x2+(100−x)2 is minimum.
So, required number are 50 and 50.
Hence, this is the answer.