Question

the sum of two positive number is 24 find the number of that the sum of their square is minimum​

Answer 1

Answer:

for minimum value DS/DX =0 then

the value of x and y is 12

Answer 2

Answer:

The two numbers are 12,12 such that their sum of the square is minimum.

Step-by-step explanation:

• The sum of the square is minimum is shown by the use of differentiation.

Step 1 of 2:

• Let the one number is x
• The second number is $24-x$
• the equation of the sum of the square is given by

    $y=x^2+(24-x)^2$

• Differentiate the equation w.r.t x

     $\frac{dy}{dx} =2x+2(24-x)(-1)\\\frac{dy}{dx} =2x+2x-48\\\frac{dy}{dx} =4x-48$

• Equate $\frac{dy}{dx} =0$

       $4x-48=0\\x=12$

Step 2 of 2:

• To prove y is minimum, differentiate again.

     $\frac{d^2y}{d^2x} =4$

• Since the double derivative is positive,y is minimum.
• Therefore,The two numbers are 12,12 such that their sum of the square is minimum