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vishal011998 Group Title

if x²>a² then x>a and x<-a how?

  • 7 months ago
  • 7 months ago

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  1. cebroski Group Title
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    It is not true that x<-a

    • 7 months ago
  2. cebroski Group Title
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    For example, if x=10 and a=2, then 10² > 2² because 100 > 4, but 10 < -2 is not true.

    • 7 months ago
  3. cebroski Group Title
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    However, perhaps you meant to say -x < -a?

    • 7 months ago
  4. liliegirl Group Title
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    You can prove that using absolute value... That's what I learn from our analytic geometry class... :))

    • 7 months ago
  5. vishal011998 Group Title
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    Yeah thanx@cebroski but i asked as it was used by friend to solve an answer...

    • 7 months ago
  6. ParthKohli Group Title
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    Take the square root of both sides.

    • 7 months ago
  7. ParthKohli Group Title
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    sqrt(x^2) = |x|

    • 7 months ago
  8. ParthKohli Group Title
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    Hence |x| > |a| Take cases

    • 7 months ago
  9. ParthKohli Group Title
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    If x>0 and a>0 then x>a If x<0 and a>0 then -x>a If x<0 and a<0 then x<a

    • 7 months ago
  10. ParthKohli Group Title
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    There really is no statement that sums up all three except |x| > |a|

    • 7 months ago
  11. triciaal Group Title
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    x^2 is positive and (-a)^2 is positive x is less than -a so you a squaring a "bigger negative number" for ex -5 is <-2 (-5)^2 >(-2)^2 5 is bigger than 2

    • 7 months ago
  12. RolyPoly Group Title
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    Consider x²>a² x² - a² > 0 (x-a)(x+a) > 0 So, we know the zeros are a and -a. Now, draw a graph for x² - a² = 0 (please forgive my poor drawing) |dw:1389442252543:dw|

    • 7 months ago
  13. RolyPoly Group Title
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    Since x² - a² > 0, we can shade the regions which are bounded by x² - a² = 0 and x-axis with *POSITIVE* y. We get: |dw:1389442338672:dw|

    • 7 months ago
  14. RolyPoly Group Title
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    Now, just like solving linear inequality, we have x < -a, *or* x>a as the solution.

    • 7 months ago
  15. RolyPoly Group Title
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    Note that since we are NOT looking for the overlapping part as the solution, we are NOT using "and" when we write the solution, i.e. "x>a and x<-a". Instead, we need to use *OR* when we write the solution, i.e. x>a *or* x<-a.

    • 7 months ago
  16. RolyPoly Group Title
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    So, in @cebroski 's example, even though x>-a is NOT true when x=10 and a=2, it is TRUE that x>a when x=10 and a=2. Therefore, the solution still holds for the quadratic inequality.

    • 7 months ago
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