Question
Solve the equation
r1=0,r2=41
Alternative Form
r1=0,r2=0.25
Evaluate
r2=4r3
Move the expression to the left side
r2−4r3=0
Factor the expression
r2(1−4r)=0
Separate the equation into 2 possible cases
r2=01−4r=0
The only way a power can be 0 is when the base equals 0
r=01−4r=0
Solve the equation
More Steps

Evaluate
1−4r=0
Move the constant to the right-hand side and change its sign
−4r=0−1
Removing 0 doesn't change the value,so remove it from the expression
−4r=−1
Change the signs on both sides of the equation
4r=1
Divide both sides
44r=41
Divide the numbers
r=41
r=0r=41
Solution
r1=0,r2=41
Alternative Form
r1=0,r2=0.25
Show Solution

Rewrite the equation
16x6+48x4y2+48x2y4+16y6=x4+2x2y2+y4
Evaluate
r2=4r3
Rewrite the expression
r2−4r3=0
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
x2+y2−4r3=0
Simplify the expression
−4r3=−x2−y2
Evaluate
−4r2×r=−x2−y2
Evaluate
−4(x2+y2)r=−x2−y2
Square both sides of the equation
(−4(x2+y2)r)2=(−x2−y2)2
Evaluate
(−4(x2+y2))2r2=(−x2−y2)2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
(−4(x2+y2))2(x2+y2)=(−x2−y2)2
Use substitution
(16x4+32x2y2+16y4)(x2+y2)=(−x2−y2)2
Evaluate the power
(16x4+32x2y2+16y4)(x2+y2)=(x2+y2)2
Solution
16x6+48x4y2+48x2y4+16y6=x4+2x2y2+y4
Show Solution
