Question 329537: I am having a hard time figuring this out and I cannot come up with any possible solution for this problem.
the directions say to solve the following inequality:
x^2-2x-5>0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve the following inequality:
x^2-2x-5>0
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You do not solve an inequality directly; you solve for
the boundary of the inequality, which is an equality.
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Solve x^2-2x-5 = 0
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x = [2 +- sqrt(4-4*1*-5)]/2
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x = [2 +- sqrt(24)]/2
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x = [1 +- sqrt(6)]
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x = 1-sqrt(6) is approximately -1.45
x = 1+sqrt(6) is approximately 3.45
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Mark those x-values on a number line.
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Now that you have the boundary values,
find the solution set for the inequality
by checking a test point from each of
the three resulting intervals of the
number line.
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x^2-2x-5>0
Check x = -10 to get: 100-20-5> 0 : true, so solution in (-inf,1-sqrt(6))
Check x = 0 to get 0+0-5 > 0 : false, so no solutions between the zeroes
Check x = +10 to get 100 -20-5 > 0: true, so solutions in (1+sqrt(6),+inf)
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Soltuion: (-inf,1-sqrt(6))U(1+sqrt(6),+inf)
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Cheers,
Stan H.
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