We have :
x^2+xy+y^2=3 and
y^2+yz+z^2=16
A=xy+yz+zx
Find the maximum value of
A.
Find x, y and z when A=max value.
(Remember the category)
(In reply to
Who can do this ? by vohonam)
I actually could solve this problem, but am too lzy to go through the process, which is as follows.
Set y=parameter "a"
Then using the quadratic formula, you can pop out 2 values (dependant on a) for each of x and z. This gives four possible situations. Evaluate each equation in "a" for the xy +yz+zx line, take the derivative and solve for zero. substitute back in to x,y, and z, and compare the four situations, one must be the answer. Performing this numerically gives the max to be 8, with x approx 1.26. (This assumed that x>0 which may not be true, so it may be larger still. But definitely larger than root 61.
re: Who can do this ?
