5.2E: Exercises
- Page ID
- 104853
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Practice Makes Perfect
In the following exercises, solve.
- \(\sqrt{5 x-6}=8\)
- \(\sqrt{5 x+1}=-3\)
- \(\sqrt[3]{2 x}=-2\)
- \(\sqrt{2 m-3}-5=0\)
- \(\sqrt{6 v-2}-10=0\)
- \(\sqrt{4 m+2}+2=6\)
- \(\sqrt{2 u-3}+2=0\)
- \(\sqrt{u-3}+3=u\)
- \(\sqrt{r-1}=r-1\)
- \(\sqrt[3]{6 x+4}=4\)
- \(\sqrt[3]{4 x+5}-2=-5\)
- \((6 x+1)^{\frac{1}{2}}-3=4\)
- \((8 x+5)^{\frac{1}{3}}+2=-1\)
- \((12 x-3)^{\frac{1}{4}}-5=-2\)
- \(\sqrt{x+1}-x+1=0\)
- \(\sqrt{z+100}-z=-10\)
- \(3 \sqrt{2 x-3}-20=7\)
- \(2 \sqrt{8 r+1}-8=2\)
- Answer
-
- \(x=14\)
- no solution
- \(x=-4\)
- \(m=14\)
- \(v=17\)
- \(m=\frac{7}{2}\)
- no solution
- \(u=3, u=4\)
- \(r=1, r=2\)
- \(x=10\)
- \(x=-8\)
- \(x=8\)
- \(x=-4\)
- \(x=7\)
- \(x=3\)
- \(z=21\)
- \(x=42\)
- \(r=3\)
In the following exercises, solve.
- \(\sqrt{3 u+7}=\sqrt{5 u+1}\)
- \(\sqrt{8+2 r}=\sqrt{3 r+10}\)
- \(\sqrt[3]{5 x-1}=\sqrt[3]{x+3}\)
- \(\sqrt[3]{2 x^{2}+9 x-18}=\sqrt[3]{x^{2}+3 x-2}\)
- \(\sqrt{a}+2=\sqrt{a+4}\)
- \(\sqrt{u}+1=\sqrt{u+4}\)
- \(\sqrt{a+5}-\sqrt{a}=1\)
- \(\sqrt{2 x+1}=1+\sqrt{x}\)
- \(\sqrt{2 x-1}-\sqrt{x-1}=1\)
- \(\sqrt{x+7}-\sqrt{x-5}=2\)
- Answer
-
- \(u=3\)
- \(r=-2\)
- \(x=1\)
- \(x=-8, x=2\)
- \(a=0\)
- \(u=\frac{9}{4}\)
- \(a=4\)
- \(x=0\: x=4\)
- \(x=1\: x=5\)
- \(x=9\)
- Explain why an equation of the form \(\sqrt{x}+1=0\) has no solution.
-
- Solve the equations \(\sqrt{r+4}-r+2=0\).
- Explain why one of the "solutions" that was found was not actually a solution to the equation.
- Answer
-
29-30. Answers will vary.