Solve x^2-4x y^2-9y 13<= 0

Evaluate

x^{2} - 4 x y^{2} - 9 y \times 13 \leq 0

Multiply the terms

x^{2} - 4 x y^{2} - 117 y \leq 0

Rewrite the expression

x^{2} - 4 y^{2} x - 117 y \leq 0

Move the constant to the right side

x^{2} - 4 y^{2} x \leq 0 - (- 117 y)

Add the terms

x^{2} - 4 y^{2} x \leq 117 y

Add the same value to both sides

x^{2} - 4 y^{2} x + 4 y^{4} \leq 117 y + 4 y^{4}

Evaluate

x^{2} - 4 y^{2} x + 4 y^{4} \leq 4 y^{4} + 117 y

Evaluate

(x - 2 y^{2})^{2} \leq 4 y^{4} + 117 y

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

(x - 2 y^{2})^{2} \leq 4 y^{4} + 117 y

Calculate

x - 2 y^{2} \leq 4 y^{4} + 117 y

Separate the inequality into 2 possible cases

{x - 2 y^{2} \leq 4 y^{4} + 117 y x - 2 y^{2} \geq - 4 y^{4} + 117 y

Calculate

{x \leq 4 y^{4} + 117 y + 2 y^{2} x - 2 y^{2} \geq - 4 y^{4} + 117 y

Calculate

{x \leq 4 y^{4} + 117 y + 2 y^{2} x \geq - 4 y^{4} + 117 y + 2 y^{2}

Solution

x \leq 4 y^{4} + 117 y + 2 y^{2} \cap x \geq - 4 y^{4} + 117 y + 2 y^{2}

Solve the inequality