Answer:
[tex]x1=\sqrt{216} \ and \ y1=\ \sqrt{216}[/tex]
Step-by-step explanation:
Let the first number is x1 and other number is y1 then
[tex]x1 * y1 =216[/tex]
Therefore
[tex]y1=[/tex][tex]\frac{216}{x1}[/tex]
also there sum is
[tex]s1 =x1+y1[/tex]....Eq(1)
Putting the value of y1 in the previous equation
[tex]s1\ =x1 + \frac{216}{x1}[/tex]........Eq(2)
Differentiate the the Eq(2) with respect to x1 we get
[tex]\frac{ds1}{dx1} \ =\ 1+216*\frac{1}{-x1^{2} }[/tex]
[tex]\frac{ds1}{dx1} \ =\ 1-\frac{216}{x1^{2} }\ =\ 0[/tex]
[tex]{x1^{2} }\ =\ 216\\ x1=\sqrt{216}[/tex]
Putting the value of X1 in Eq(1) we get
[tex]y1=\frac{216}{\sqrt{216} } \\y1=\frac{216*\sqrt{216} }{216} \\y1=\ \sqrt{216}[/tex]
So [tex]x1=\sqrt{216} \ and \ y1=\ \sqrt{216}[/tex]
