maths
posted by prateek
show that the lines x^4xy+y^=0 and x+y=1 form an equilateral triangle and find its area

Steve
If that's x^2  4xy + y^2 = 0, that means that
y = (2+√3)x and y = (2√3)x
Find where those lines intersect y = x + 1
A: (2+√3)x = 1x
x = 1/(3+√3)
y = 1x = (2+√3)/(3+√3)
B:(2√3)x = 1x
x = 1/(3√3)
y = 1  x = (2√3)/(3√3)
After a little algebra, we find that
OA^{2} = 2/3
OB^{2} = 2/3
AB^2 = √6/3
The altitude = 1/√2, so the area of OAB = 1/2 * 1/√2 * √6/3 = √3/6 
Steve
That's AB = √6/3
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