x+y-z=15

z* y=18

y * x + x = 48

asked by guest
on Sep 20, 2024 at 6:41 am



You asked:

Solve the system of equations:\[\begin{aligned}x + y - z &= 15\\z y &= 18\\y x + x &= 48\end{aligned}\]

MathBot Answer:

The system of equations has \(3\) solutions.

\[x = - \frac{1895 \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{10443} - \frac{169 \sqrt[3]{343 + 18 \sqrt{997}}}{177} - \frac{\sqrt{997} \sqrt[3]{343 + 18 \sqrt{997}}}{59} + \frac{46}{3} + \frac{23 \sqrt{997} \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{3481}, y = - \frac{5 \sqrt{997} \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{3481} - \frac{8 \sqrt[3]{343 + 18 \sqrt{997}}}{177} + \frac{14}{3} + \frac{\sqrt{997} \sqrt[3]{343 + 18 \sqrt{997}}}{59} + \frac{866 \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{10443}, z = - \sqrt[3]{343 + 18 \sqrt{997}} + 5 + \frac{59}{\sqrt[3]{343 + 18 \sqrt{997}}}\]\[x = - \frac{23 \sqrt{997} \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} + \frac{\sqrt{997} \sqrt[3]{343 + 18 \sqrt{997}}}{118} + \frac{169 \sqrt[3]{343 + 18 \sqrt{997}}}{354} + \frac{1895 \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{20886} + \frac{46}{3} - \frac{23 \sqrt{2991} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} - \frac{169 \sqrt{3} i \sqrt[3]{343 + 18 \sqrt{997}}}{354} - \frac{\sqrt{2991} i \sqrt[3]{343 + 18 \sqrt{997}}}{118} + \frac{1895 \sqrt{3} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{20886}, y = - \frac{433 \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{10443} - \frac{\sqrt{997} \sqrt[3]{343 + 18 \sqrt{997}}}{118} + \frac{4 \sqrt[3]{343 + 18 \sqrt{997}}}{177} + \frac{5 \sqrt{997} \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} + \frac{14}{3} - \frac{433 \sqrt{3} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{10443} - \frac{4 \sqrt{3} i \sqrt[3]{343 + 18 \sqrt{997}}}{177} + \frac{5 \sqrt{2991} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} + \frac{\sqrt{2991} i \sqrt[3]{343 + 18 \sqrt{997}}}{118}, z = 5 - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{343 + 18 \sqrt{997}} + \frac{59}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{343 + 18 \sqrt{997}}}\]\[x = - \frac{23 \sqrt{997} \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} + \frac{\sqrt{997} \sqrt[3]{343 + 18 \sqrt{997}}}{118} + \frac{169 \sqrt[3]{343 + 18 \sqrt{997}}}{354} + \frac{1895 \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{20886} + \frac{46}{3} - \frac{1895 \sqrt{3} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{20886} + \frac{\sqrt{2991} i \sqrt[3]{343 + 18 \sqrt{997}}}{118} + \frac{169 \sqrt{3} i \sqrt[3]{343 + 18 \sqrt{997}}}{354} + \frac{23 \sqrt{2991} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962}, y = - \frac{433 \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{10443} - \frac{\sqrt{997} \sqrt[3]{343 + 18 \sqrt{997}}}{118} + \frac{4 \sqrt[3]{343 + 18 \sqrt{997}}}{177} + \frac{5 \sqrt{997} \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} + \frac{14}{3} - \frac{\sqrt{2991} i \sqrt[3]{343 + 18 \sqrt{997}}}{118} - \frac{5 \sqrt{2991} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{6962} + \frac{4 \sqrt{3} i \sqrt[3]{343 + 18 \sqrt{997}}}{177} + \frac{433 \sqrt{3} i \left(343 + 18 \sqrt{997}\right)^{\frac{2}{3}}}{10443}, z = 5 + \frac{59}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{343 + 18 \sqrt{997}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{343 + 18 \sqrt{997}}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

+ Submit Question