Solve x< x^2 y^2 - ScanMath

Evaluate

x < x^{2} y^{2}

Rewrite the expression

x < y^{2} x^{2}

Add or subtract both sides

x - y^{2} x^{2} < 0

Evaluate

x^{2} - \frac{1}{y ^{2}} \times x < 0

Add the same value to both sides

x^{2} - \frac{1}{y ^{2}} \times x + \frac{1}{( 2 y ^{2} ) ^{2}} < \frac{1}{( 2 y ^{2} ) ^{2}}

Evaluate

(x - \frac{1}{2 y ^{2}})^{2} < \frac{1}{( 2 y ^{2} ) ^{2}}

Take the 2 -th root on both sides of the inequality

(x - \frac{1}{2 y ^{2}})^{2} < \frac{1}{( 2 y ^{2} ) ^{2}}

Calculate

x - \frac{1}{2 y ^{2}} < \frac{1}{2 y ^{2}}

Separate the inequality into 2 possible cases

{x - \frac{1}{2 y ^{2}} < \frac{1}{2 y ^{2}} x - \frac{1}{2 y ^{2}} > - \frac{1}{2 y ^{2}}

Calculate

More Steps

{x < \frac{1}{y ^{2}} x - \frac{1}{2 y ^{2}} > - \frac{1}{2 y ^{2}}

Cancel equal terms on both sides of the expression

{x < \frac{1}{y ^{2}} x > 0

Solution

x \in (0, + \infty) \cap x < \frac{1}{y ^{2}}

Solve the inequality