Solve u + v = u^2 + v^2

Evaluate

u + v = u^{2} + v^{2}

Move the expression to the left side

u + v - (u^{2} + v^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

u + v - u^{2} - v^{2} = 0

Simplify

u + v - v^{2} - u^{2} = 0

Rewrite in standard form

- u^{2} + u + v - v^{2} = 0

Multiply both sides

u^{2} - u - v + v^{2} = 0

Substitute a= 1,b= - 1 and c= - v + v^{2} into the quadratic formula u = \frac{- b \pm b ^{2} - 4 a c}{2 a}

u = \frac{1 \pm ( - 1 ) ^{2} - 4 ( - v + v ^{2} )}{2}

Simplify the expression

More Steps

u = \frac{1 \pm 1 + 4 v - 4 v ^{2}}{2}

Solution

u = \frac{1 + 1 + 4 v - 4 v ^{2}}{2} u = \frac{1 - 1 + 4 v - 4 v ^{2}}{2}

U + v = u^2 + v^2

Solve the equation

$Solve for u$

$Solve for v$