Just a few important notes from this chapter...
- A variable with an even exponent has two solutions always. Treat it with caution.
Example: x^2 = 25. Therefore, x = ±25
- You can afford to loosen up with variables with odd exponents as they always have only one solution.
- Common Bases or Common Exponents
- When you come across an equation with exponents on either side, it is imperative that you convert the equation into one with either a common base or common exponent.
- Once you've done this the common base can be cancelled to equate the exponents on either side to form the solution.
- Eliminating the square root by squaring both sides:
- This is a simple method of solving problems with a square root in the equation
- However, take care when squaring as this can sometimes introduce an extraneous solution where there are two solutions.
- Finally substitute all the solutions in the main equation to find the actual solution as only one solution will work in the main equation.
- Also, the square root symbol works only on positive numbers and yield only positive numbers for results. The square root of a negative number is undefined and is not tested by the GMAT.
- All the same, the square root of a positive number can either be a negative or a positive number.
- Cube Roots
- To solve Cube roots, cube both sides to find a solution.
- Remember, a cube root retains the original sign of the number and hence does not introduce any extraneous solution.
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