F.4 MATHS

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A=7x-x^2 ,x+y=7 ,xy=A

a.Find the possible values of x in surd form when A=9
A = 7x-x^2, A = 9
9 = 7x-x^2
x^2-7x+9 = 0
x = {7 +/- sqrt[(-7)^2-4(1)(9)]}/2
x = 7/2 +/- sqrt(13)/2

b.Find the max. possible A and the corresponding value of x
x+y=7
Therefore, y = 7-x
xy=A
Therefore, x(7-x) = A => 7x-x^2 = A
A=7x-x^2
A = (7/2)^2 - (7/2)^2 + 7x - x^2
A = (7/2)^2 - (7/2 - x)^2
A is maximum when (7/2 - x)^2 = 0
Therefore, maximum A is 49/4 when x is 7/2