Question

х
11. Find two numbers x and y such that xy, x/y , x + y
are equal​

Answer 1

Step-by-step explanation:





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Class 12

>>Applied Mathematics

>>Application of Derivatives

>>Applications of Maxima and Minima

>>Find two positive numbers x and y such t

Question



Find two positive numbers x and y such that x+y=60 and xy3 is maximum.

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Solution



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Let P=xy3

It is given that x+y=60

⇒x=60−y

P=(60−y)y3   [Putting value of x]

    =60y3−y4

⇒dydP=180y2−4y3

dy2d2P=360y−12y2

For maximum or minimum values of y, P we have

dydP=0

⇒180y2−4y3=0

⇒4y2(45−y)=0

⇒y=0