Solve x^2p^2 + y^2 q^2 = z^2

Evaluate

x^{2} p^{2} + y^{2} q^{2} = z^{2}

Rewrite the expression

p^{2} x^{2} + y^{2} q^{2} = z^{2}

Move the expression to the right-hand side and change its sign

p^{2} x^{2} = z^{2} - y^{2} q^{2}

Divide both sides

\frac{p ^{2} x ^{2}}{p ^{2}} = \frac{z ^{2} - y ^{2} q ^{2}}{p ^{2}}

Divide the numbers

x^{2} = \frac{z ^{2} - y ^{2} q ^{2}}{p ^{2}}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{z ^{2} - y ^{2} q ^{2}}{p ^{2}}

Simplify the expression

More Steps

x = \pm \frac{z ^{2} - y ^{2} q ^{2}}{∣ p ∣}

Separate the equation into 2 possible cases

x = \frac{z ^{2} - y ^{2} q ^{2}}{∣ p ∣} x = - \frac{z ^{2} - y ^{2} q ^{2}}{∣ p ∣}

Calculate

x = \frac{z ^{2} - q ^{2} y ^{2}}{∣ p ∣} x = - \frac{z ^{2} - y ^{2} q ^{2}}{∣ p ∣}

Solution

x = \frac{z ^{2} - q ^{2} y ^{2}}{∣ p ∣} x = - \frac{z ^{2} - q ^{2} y ^{2}}{∣ p ∣}

Solve the equation