IB DP Maths: AA HL复习笔记2.4.2 Solving Equations

How can I solve equations analytically where the unknown appears only once?

• These equations can be solved by rearranging
• For one-to-one functions you can just apply the inverse
  • Addition and subtraction are inverses
• Always check your solutions by substituting back into the original equation

How can I solve equations analytically where the unknown appears more than once?

• Sometimes it is possible to simplify expressions to make the unknown appear only once
• Collect all terms involving x on one side and try to simplify into one term
  • How can I solve equations analytically when the equation can't be simplified?

• Sometimes it is not possible to simplify equations
• Most of these equations cannot be solved analytically
• A special case that can be solved is where the equation can be transformed into a quadratic using a substitution
  • These will have three terms and involve the same type of function
• Identify the suitable substitution by considering which function is a square of another

Can I divide both sides of an equation by an expression?

• When dividing by an expression you must consider whether the expression could be zero
• Dividing by an expression that could be zero could result in you losing solutions to the original equation

How can I solve equations graphically?

Why do I need to solve equations graphically?

• Some equations cannot be solved analytically