Update equations.js

adv-math/src/equation-solvers/equations.js

@@ -18,6 +18,48 @@ class Equations {
         const x2 = (-b - sqrtDiscriminant) / (2 * a);
         return [x1, x2];
     }
+
+    // Method to solve a cubic equation of the form: ax^3 + bx^2 + cx + d = 0
+    static solveCubic(a, b, c, d) {
+        // Implementation of Cardano's method to solve cubic equations
+        if (a === 0) {
+            throw new Error('The coefficient of x^3 cannot be zero.');
+        }
+
+        const delta0 = b * b - 3 * a * c;
+        const delta1 = 2 * b * b * b - 9 * a * b * c + 27 * a * a * d;
+        const C = Math.cbrt((delta1 + Math.sqrt(delta1 * delta1 - 4 * delta0 * delta0 * delta0)) / 2);
+        const x1 = -(1 / (3 * a)) * (b + C + delta0 / C);
+        return [x1];
+    }
+
+    // Method to solve an exponential equation of the form: a^x = b
+    static solveExponential(a, b) {
+        if (a <= 0 || a === 1 || b <= 0) {
+            throw new Error('Values of a and b must be positive, and a cannot be equal to 1.');
+        }
+        return Math.log(b) / Math.log(a);
+    }
+
+    // Method to solve a logarithmic equation of the form: log_a(bx + c) = d
+    static solveLogarithmic(a, b, c, d) {
+        if (a <= 0 || a === 1 || b <= 0 || c < 0) {
+            throw new Error('Values of a, b, and c must be positive, and a cannot be equal to 1.');
+        }
+        const logValue = d / Math.log(a);
+        return (Math.pow(a, logValue) - c) / b;
+    }
+
+    // Method to solve a system of linear equations
+    static solveLinearSystem(a1, b1, c1, a2, b2, c2) {
+        const determinant = a1 * b2 - a2 * b1;
+        if (determinant === 0) {
+            throw new Error('The system of equations has no unique solution.');
+        }
+        const x = (c1 * b2 - c2 * b1) / determinant;
+        const y = (a1 * c2 - a2 * c1) / determinant;
+        return [x, y];
+    }
 }
 
 module.exports = Equations;