Question

x+y=6 please give me answer​

Answer 1

Answer:

but what we have to find.please rewrite the question

Answer 2

Calculus Method:

Given, x+y = 6. Transposing x to RHS,

y = 6 - x

Substituting for y=6 - x,

xy = x(6-x) = 6x - x² = f(x), suppose……………………………………………..(1)

To find the maximum value

x + y = 6 can be written as y = 6 - x

Now, put this value in xy

xy can be written as x(6 - x) = w(say)

or, w=6x−x2

Now, differentiate above equation wrt x and equating it to zero;

dw/dx=6−2x=0

We get, x = 3

Now if the second derivative of w is negative at x = 3, means w will be maximum at that point.

d2w/dx2=−2

So, w will be maximum at x = 3 and y = 6–x = 6–3 = 3

w(max) = xy = 3 * 3 = 9

Short method:

If sum of two variables is a constant, then the product of both numbers will be maximum when both the numbers are equal.

x + y = 6

product of x and y will be maximum when x = y = 6/2 = 3.