Given x2 + y2 = 1, find the maximum and minimum of 2x + y Maximum value related to circle

Given x2 + y2 = 1, find the maximum and minimum of 2x + y Maximum value related to circle

Let 2x + y = a
y=a-2x
Substituting X & # 178; + Y & # 178; = 1
5x²-4ax+a²-1=0
If x is a real number, then △ > = 0
16a²-20a²+20>=0
a²

x2+y2+2xy=256 x2+y2-2xy=4 (x2,

X2 + Y2 + 2XY = 256 (x + y) = 256 x + y = ± 16 x2 + y2-2xy = 4 (X-Y) = 4 X-Y = ± 2 you ask how to do it, I don't quite understand what you mean, is to seek the value of X and y, or what? Thank you for adopting, if you don't understand, please ask
Thank you!

First simplify and then evaluate x2-y2 / x2-2xy + Y2, where x = 110 and y = 10 (all are the squares of X and y)

The original formula = (x2-2xy + Y2) - Y2 / x2 = (X-Y) 2-y2 / x2 = (X-Y + Y / x) (x-y-y / x)

How to transform x2 + 8 + Y2 into x2 + 2XY + Y2? (2 is square)

Using y = 4 / X
So xy = 4
So 8 = 2XY
So x & sup2; + 8 + Y & sup2; = x & sup2; + 2XY + Y & sup2;