(x² + y² -z2)2 - (2xy)2
Answers
x+y=2 Equation 1
x²+y²=2 Equation 2
Find:
xy
Solution:
The approach to a system of 2 equations with two unknowns is to ascertain if they are independent, and then use either substitution or elimination.
As to independence, Equation 1 can be rewritten in Slope-Intercept form as y = -x + 2. So this is a negative sloping line, m= -1, passing through point (0, 2). The circle is centered at the origin and has a radius of sqrt(2). At a 45-degree angle, this circle should pass through the point (1, 1) which is on the line so we’re pretty sure this is a solution. Let’s do the substitution as a check.
Step 1
Substitute the value of y from Equation 1 into Equation 2 and solve for x.
x²+y²=2
x²+(-x + 2)²=2
x²+x²-4x+4=2
x²-2x+2=1
x²-2x+1=0
(x-1)(x-1)=0
x-1=0
x=1
Substitute x = 1 into either equation and solve for y.
y = -x + 2
y = -(1) + 2
y = 1
Answer:
xy = 1(1) = 1