By George Boole

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Extra info for A Treatise on Differential Equations

Example text

The resulting expression is similar to y (y – y – 6), which factors into y (y + 2)(y – 3). Similarly, you can factor into , and then set each factor equal to 0 and solve. Here’s the solution set: x=0 k Solve for x in . The answer is x = 28. Isolate the radical by adding 5 to each side of the equation to get . Then square both . This equation simplifies to x – 3 = 25, sides to get rid of the square root, like so: which is the same as x = 28. It is easy to see that x = 28 is indeed a solution. 35 Chapter 2: Real Numbers Come Clean l .

Simplify Solve It . Chapter 2: Real Numbers Come Clean Answers to Problems on Real Numbers This section contains the answers for the practice problems presented in this chapter. We suggest you read the following explanations if your answers don’t match up with ours (or if you just want a refresher on solving a particular type of problem). a Solve for x in . The answer is x > 8 or x < –4. Start by dropping the absolute value bars and setting up your two inequalities: 4 – 2x > 12 or 4 – 2x < –12.

X = 0, 16 . Q. Solve for x in A. x=5 Start this one by subtracting 4 from both sides of the equation to isolate the radi. Next, square each cal: side to get rid of the square root. So becomes 2x – 1 = (x – 2)(x – 2). Note: A common mistake is to forget that (x – 2)2 is (x – 2)(x – 2) and not x2 + 4, nor x2 – 4; don’t fall for this. Don’t let this one scare you! Just remember your basic fraction rules and look for a pattern for factoring. Start by factoring out the x. Doing so leaves you with . (Remember that .