Question

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

Answer 1

Given :-

Sum of two positive square = 15

Need to find :-

Sum of whose squares is minimum.

Solution :-

Let the sum be x and y

x + y = 15

y = 15 - x[1]

Minimum value.

$\bf x^2+y^2$

Putting y as 15 - x

$\sf x^2 + {\bigg(15-x\bigg)}^{2}$

Now,

$\sf 2x - \bigg( 2(15 - x)\bigg)$

$\sf 2x -\bigg(30 - 2x\bigg)$

2x - 30 + 2x = 0

2x + 2x - 30 = 0

4x - 30 = 0

x = 30/4 = 15/2

Therefore - 15/2 and 15/2 are the two minimum square

Answer 2

$\mapsto\bf{Given :-}$

Sum of two positive square = 15

$\mapsto\bf{find :-}$

Sum of whose squares is minimum.

$\mapsto\bf{Let's \:do\: it :-}$

Let the sum be x and y

➦$\sf x + y = 15$

➦$\sf y = 15 - x [1]$

$\underline{\bf{Minimum\: value.}}$

$\bf x^2+y^2x$

$\underline{\bf{Putting\: y \:as\: 15 - x}}$

$\sf x^2 + {\bigg(15-x\bigg)}^{2}$

$\mapsto\bf{Now,}$

$\sf 2x - \bigg( 2(15 - x)\bigg)2x−(2(15−x))$

$\sf 2x -\bigg(30 - 2x\bigg)2x−(30−2x)$

➦ $\sf 2x - 30 + 2x = 0$

➦$\sf 2x + 2x - 30 = 0$

➦$\sf 4x - 30 = 0$

★$\bold{\boxed{x = 30/4 = 15/2}}$★

$\sf\color{lime}Therefore\: - 15/2\: and\: 15/2\: are\: the\: two\: minimum\: square$

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Thankyou :)