Biquadratic Equations
Biquadratic equations, also known as quartic equations, are equations of the form x² + 2x²-3=0, where t = x². To solve these equations, we use the formula t = x² +²+ 2+ 3 = 0. By applying the quadratic formula t = -b ± √(b²-4ac) / 2a, we can find the solutions for the equation.
Equations of Degree Higher Than 2
Moving on to equations of a degree higher than 2, we encounter equations like 10-32, 1 1 1-2, and 1 11-20, which require different methods to solve. For example, in the equation 3x²-3x+2=0, the solution is found to be (x-1) (x-1)⋅ (x+2).
Rational Equations
Rational equations, such as the one represented by 4x/X+2X-2 =-2:44, can also be solved using methods like Ruffini.
Irrational Equations
When dealing with equations containing irrational numbers, such as √3x+16=2x-1, we must follow a different approach to find the solution. Consequently, the equation -4x² + 7x +15=0 can be solved to obtain x=-7√(7)³²-4 (-4). (15)/2(-4).
Exponential and Logarithmic Equations
In equations that involve exponents and logarithms, we have to consider equations like .34×-2 and log[(x+1)-5] = log (x-3). Each of these equation types has its own suited method of solving.
Systems of Linear Equations
Solving systems of linear equations, regardless of their specific type, can be done using methods like reduction, substitution, and equalization.
Systems of Non-Linear Equations
In cases where the equations are non-linear, methods like substitution come in handy to find the solutions.
Graphically Solving Equations
Solving equations by plotting their graphs can be a helpful method for better visualization and understanding of the solutions.
Summary
In conclusion, we have explored a variety of equations, including biquadratic, rational, irrational, exponential, logarithmic, and systems of equations. Each of these equation types requires a different approach and method to solve. Whether it's using mathematical formulas, algebraic techniques, or graphical representation, the process of finding solutions varies depending on the type of equation we are dealing with.
