$\sqrt{4356x^2-4356y^2+11664}$

asked by guest
on May 05, 2024 at 6:23 pm

You asked:

Evaluate the expression: \(\sqrt{4356 \cdot {x}^{2} - 4356 \cdot {y}^{2} + 11664}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{4356 \cdot {x}^{2} - 4356 \cdot {y}^{2} + 11664} = \sqrt{4356 x^{2} - 4356 y^{2} + 11664} \)

Expanded

\[\sqrt{4356 \cdot {x}^{2} - 4356 \cdot {y}^{2} + 11664} = \sqrt{4356 x^{2} - 4356 y^{2} + 11664}\]

Factored

\[\sqrt{4356 \cdot {x}^{2} - 4356 \cdot {y}^{2} + 11664} = 6 \sqrt{121 x^{2} - 121 y^{2} + 324}\]

Roots

\[\sqrt{4356 \cdot {x}^{2} - 4356 \cdot {y}^{2} + 11664} = i \sqrt[4]{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)} + \sqrt[4]{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)} \approx 108.0 i \left(0.557879896357263 \left(\operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(0.373456790123457 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.373456790123457 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)} + 108.0 \left(0.557879896357263 \left(\operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(0.373456790123457 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.373456790123457 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)}\]\[\sqrt{4356 \cdot {x}^{2} - 4356 \cdot {y}^{2} + 11664} = i \left(- \sqrt[4]{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)}\right) - \sqrt[4]{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)} \approx - 108.0 i \left(0.557879896357263 \left(\operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(0.373456790123457 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.373456790123457 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)} - 108.0 \left(0.557879896357263 \left(\operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(0.373456790123457 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 0.373456790123457 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.373456790123457 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8712 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 8712 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},4356 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4356 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4356 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4356 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 11664 \right)}}{2} \right)}\]

asked 12 days ago

active 12 days ago