The solution set is {3, 3}. Or, we can solve an equation like x2 9 using the square root property as we will see in Example 1a). Definition The Square Root Property Let k be a constant. If x 2 k, then x 1k or x 1k. (The solution is often written as x 1k, read as “x equals plus or minus the square root of k.”) Note We can use the square root property to solve an equation containing a squared quantity and a constant. To do so we will get the squared quantity containing the variable on one side of the equal sign and the constant on the other side. Solve using the square root property. a) x2 9 b) t2 20 0 c) 2a2 21 3 Solution a) x2 9 b R x 19 or x 19 Square root property x 3 or x 3 The solution set is {3, 3}. The check is left to the student. An equivalent way to solve x2 9 is to write it as x2 9 x 19 Square root property x 3 The solution set is {3, 3}. We will use this approach when solving equations using the square root property. b) To solve t 2 20 0, begin by getting t 2 on a side by itself. t 2 20 0 t 2 20 Add 20 to each side. t 120 Square root property t 14 15 Product rule for radicals t 215 14 2 Check: t 215: t 2 20 0 t 215: t 2 20 0 (215)2 20 ? 0 (215)2 20 ? 0 (4 5) 20 ? 0 (4 5) 20 ? 0 20 20 0 ✓ 20 20 0 ✓ The solution set is 5215, 2156. EXAMPLE 1 Be sure you are writing out each step as you are reading the example. 612 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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