3.5.3 Modify

Solving an equation quite often requires the same operation to be applied to both sides of an equation, as in “square both sides”, “take the sin of both sides”, “take the log of both sides” and so on. This kind of manipulation is performed by the modify-equation tool. Selecting Modify from the menu brings up a dialog where a modification pattern can be entered. The pattern will be applied to both sides of an equation, retaining the (in)equality.

Modification patterns contain a wildcard, like that found in substitution patterns. Each occurrence of ? in a modification pattern represents the left side of the equation when the pattern is applied to the left side, and represents the right side of the equation when applied to the right side.

• To square both sides: ?^2.
• To take the square root of both sides: √?.
• To add a value to both sides: ?+value.
• To take the log of both sides: ln ?.
• To take the sin of both sides: sin ?.
• To double both sides: ?+?.

Solve the following equations by using Modify to square both sides.

• √(x-8)=3
• √(x+8)+√(x+15)=√(9⋅x+40)