Identify Extraneous Solutions to Radical Equations
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- (Video) Extraneous Solution when Solving Radical Equations by Tom McLaughlin This video by Tom McLaughlin covers extraneous solutions. Summary\large{\text{Summary}}Summary An ex…
By Alex Federspiel, Amy Feraco, Jonathan Heller
- Some radicals have extraneous solutions, or solutions that aren't valid. This means that some radicals have no solutions at all. Extraneous solutions highlight why it's SO impor…
By Hannah Bonville, Alex Federspiel, Joshua Siktar, Amy Feraco, Jonathan Heller, Anusha Rahman
- Identifying Extraneous Solutions to Radical Equations Some radicals have extraneous soulutions. These are solutions that aren't valid when plugged into the original equation. He…
By Caroline K, Jonathan Heller, Anusha Rahman
Problems 20
- Does the equation x+3−4x−1=9\sqrt{x+3} - \sqrt{4x - 1} =9x+3−4x−1=9 have real solutions?
- Solve for xxx. 2x+8=x\sqrt{2x+8}=x2x+8=x
- If 5x+4=3x,\sqrt{5x+4}=3x,5x+4=3x, what could xxx be? Select all that apply.
- Solve for xxx. 2x+11=8x+2−3\sqrt{2x+11}=\sqrt{8x+2}-32x+11=8x+2−3
- Solve for xxx. x−4=9x\sqrt{x}-4=\sqrt{9x}x−4=9x
- Solve for xxx. x−6=7x−22\sqrt{x-6}=\sqrt{7x}-22x−6=7x−22
- Find all real solutions xxx to the equation x−3=x+1\sqrt{x-3}=\sqrt{x}+1x−3=x+1.
- Solve 5x+6+3=3x+3+4\sqrt{5x+6}+3=\sqrt{3x+3}+45x+6+3=3x+3+4.
- Solve the equation x−15=3−x\sqrt{x-15}=3-\sqrt{x}x−15=3−x.
- Solve x−3=4−2x+1\sqrt{x-3}=4-\sqrt{2x+1}x−3=4−2x+1.
- Find all real numbers xxx such that 4−11x=x−2\sqrt{4-11x}=x-24−11x=x−2.
- Solve −2x−6=x+3\sqrt{-2x-6}=x+3−2x−6=x+3.
- Joe solves x−3=30−2xx-3=\sqrt{30-2x}x−3=30−2x by squaring to get (x−3)2=30−2x(x-3)^2 = 30-2x(x−3)2=30−2x, and solving the resulting quadratic. Which of the solutions to the qua…
- What is the solution set of the following equation? x+4x=3x + \sqrt{4x} = 3x+4x=3
- What is the solution set for the equation 6=x−x,6 = x - \sqrt{x},6=x−x, where xxx is a positive variable?
- What is the solution set for x+2=x2+4xx + 2 = \sqrt{x^2 + 4x}x+2=x2+4x
- What is the solution set to 2x−3=x−1?\sqrt{2x-3} = x - 1 ?2x−3=x−1?
- What is an "extraneous solution"?
- If we solved an equation involving a radical and reached the step x=−3\sqrt{x} = -3x=−3, what does that mean about the equation?
- Consider: 2x+3=x\sqrt{2x+3} = x2x+3=x The equation above has extraneous solutions. True or False?