Solve 4x^2 4y^2 17xy^5x^5y >= 1

Evaluate

4 x^{2} \times 4 y^{2} \times 17 x y^{5} x^{5} y \geq 1

Multiply

More Steps

272 x^{8} y^{8} \geq 1

Rewrite the expression

272 y^{8} x^{8} \geq 1

Divide both sides

\frac{272 y ^{8} x ^{8}}{272 y ^{8}} \geq \frac{1}{272 y ^{8}}

Divide the numbers

x^{8} \geq \frac{1}{272 y ^{8}}

Take the 8 -th root on both sides of the inequality

8 x^{8} \geq 8 \frac{1}{272 y ^{8}}

Calculate

∣ x ∣ \geq \frac{8 27 2 ^{7}}{272 ∣ y ∣}

Separate the inequality into 2 possible cases

x \geq \frac{8 27 2 ^{7}}{272 ∣ y ∣} x \leq - \frac{8 27 2 ^{7}}{272 ∣ y ∣}

Calculate

{x \geq \frac{8 27 2 ^{7}}{272 ∣ y ∣} y \neq = 0 {x \leq - \frac{8 27 2 ^{7}}{272 ∣ y ∣} y \neq = 0

Solution

x \geq \frac{8 27 2 ^{7}}{272 ∣ y ∣}, y \neq = 0 x \leq - \frac{8 27 2 ^{7}}{272 ∣ y ∣}, y \neq = 0

Solve the inequality