Question

Divide 100 into two parts such that the sum of their squares is minimum

Answer 1

$Total \: amount = 100$

$Let \: x, \: y \:are \: two \: parts$

$x + y = 100$

$\implies y = 100 - x \: ---(1)$

/* According to the problem given */

$s = x^{2} + y^{2}$

$\implies s = x^{2} + ( 100 - x )^{2} \: [From \:(1) ]$

$\implies \frac{ds}{dx} = 2x + 2(100-x)(-1)$

$\implies \frac{ds}{dx} = 0$

$\implies 2x = 2( 100 - x )$

$\implies x = ( 100 - x )$

$\implies 2x = 100$

$\implies x = 50$

/* Put x = 50 in equation (1), we get */

$y = 50$

$s_{minimum} = 50^{2} + 50^{2} \\= 2500 + 2500\\= 5000$

$s_{minimum } \: at \: x = 50 , \:y = 50$

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Answer 2

Step-by-step explanation:

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