Solve x^2 y^2=10 y=x^2 2

Question

Solve the system of equations

(x_{1}, y_{1}) = (- 450, 2) (x_{2}, y_{2}) = (0, 0) (x_{3}, y_{3}) = (450, 2)

Evaluate

{x^{2} y^{2} = 10 y 10 y = x^{2} \times 2

Use the commutative property to reorder the terms

{x^{2} y^{2} = 10 y 10 y = 2 x^{2}

Solve the equation for y

More Steps

{x^{2} y^{2} = 10 y y = \frac{x ^{2}}{5}

Substitute the given value of y into the equation x^{2} y^{2} = 10 y

x^{2} (\frac{x ^{2}}{5})^{2} = 10 \times \frac{x ^{2}}{5}

Simplify

More Steps

\frac{x ^{6}}{25} = 10 \times \frac{x ^{2}}{5}

Cancel out the common factor 5

\frac{x ^{6}}{25} = 2 x^{2}

Cross multiply

x^{6} = 25 \times 2 x^{2}

Simplify the equation

x^{6} = 50 x^{2}

Move the expression to the left side

x^{6} - 50 x^{2} = 0

Factor the expression

x^{2} (x^{4} - 50) = 0

Separate the equation into 2 possible cases

x^{2} = 0 \cup x^{4} - 50 = 0

The only way a power can be 0 is when the base equals 0

x = 0 \cup x^{4} - 50 = 0

Solve the equation

More Steps

x = 0 \cup x = 450 \cup x = - 450

Rearrange the terms

{x = 0 y = \frac{x ^{2}}{5} \cup {x = 450 y = \frac{x ^{2}}{5} \cup {x = - 450 y = \frac{x ^{2}}{5}

Calculate

More Steps

{x = 0 y = 0 \cup {x = 450 y = \frac{x ^{2}}{5} \cup {x = - 450 y = \frac{x ^{2}}{5}

Calculate

More Steps

{x = 0 y = 0 \cup {x = 450 y = 2 \cup {x = - 450 y = \frac{x ^{2}}{5}

Calculate

More Steps

{x = 0 y = 0 \cup {x = 450 y = 2 \cup {x = - 450 y = 2

Calculate

{x = - 450 y = 2 \cup {x = 0 y = 0 \cup {x = 450 y = 2

Check the solution

More Steps

{x = - 450 y = 2 \cup {x = 0 y = 0 \cup {x = 450 y = 2

Check the solution

More Steps

{x = - 450 y = 2 \cup {x = 0 y = 0 \cup {x = 450 y = 2

Check the solution

More Steps

{x = - 450 y = 2 \cup {x = 0 y = 0 \cup {x = 450 y = 2

Solution

(x_{1}, y_{1}) = (- 450, 2) (x_{2}, y_{2}) = (0, 0) (x_{3}, y_{3}) = (450, 2)

Show Solution