If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n

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rnagi2017 rnagi2017 · Answer 1 · 2017-10-23T18:03:40+02:00

If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n

2 + 2(4)

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ahirohit963 ahirohit963 · Answer 2 · 2021-11-18T06:29:54+01:00

The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.

Given :

If m and n are two positive real numbers whose product is 10.

Given that m and n are two positive real numbers whose product is 10 that is:

mn = 10

[tex]\rm m= \dfrac{10}{n}[/tex] ---- (1)

The minimum value of (m + 2n) can be determined by using the following calculation.

Put the value of m in the given expression.

[tex]\rm = \dfrac{10}{n}+2n[/tex] ---- (2)

Now for minimum value differentiate the above expression with respect to n.

[tex]\rm =-\dfrac{10}{n^2}+2[/tex]

Now equate the above equation to zero.

[tex]\rm \dfrac{10}{n^2}=2[/tex]

[tex]\rm n = \sqrt{5}[/tex]

Now, put the value of n in equation (2).

[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]

= 8.95

The minimum value of (m + 2n) is 8.95.

For more information, refer to the link given below:

https://brainly.com/question/72395