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RE: Test Your Math Skills and Win SBD # 2

in #contest7 years ago (edited)
  1. x^2 < x^4
    Let x = -1
    (-1)^2 < (-1)^4
    1 < 1 , FALSE
    Let x= -2
    (-2)^2 < (-2)^4
    4 < 16 , TRUE
    Let x = -3
    (-3)^2 < (-3)^4
    9 < 81 , TRUE
    Therefore, the inequality is FALSE for all values of x.

  2. x^3 < x^4
    Let x= -1
    (-1)^3 < (-1)^4
    -1 < 1, TRUE
    Let x= -2
    (-2)^3 < (-2)^4
    -8 < 4 , TRUE
    Let x= -3
    (-3)^3 < (-3)^4
    -27 < 9, TRUE
    Therefore, the inequality is TRUE for all values of x.

  3. x + (1/x) < 0
    Let x= -1
    (-1) + (1/(-1)) < 0
    -1 - 1 < 0
    -2 < 0 , TRUE
    Let x= -2
    (-2) + (1/(-2)) < 0
    -2 - (1/2) < 0
    -(5/2) < 0, TRUE
    Let x= -3
    (-3)+ (1/(-3)) < 0
    -3 - (1/3) < 0
    -(10/3), TRUE
    Therefore the inequality is TRUE for all values of x.

  4. x = √ x^2
    Let x= -1
    (-1) = √(-1)^2
    -1 = -1, TRUE
    Let x = -2
    (-2) = √(-2)^2
    -2 = -2, TRUE
    Let x= -3
    (-3) = √(-3)^2
    -3 = -3, TRUE
    Therefore the inequality is TRUE for all values of x.

To summarize, The inequalities of #2, #3, and #4 are TRUE except #1 which is FALSE.

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Your 4 th option explaination is wrong

Hi @satyamsoni, What makes it wrong? :D
As far as I know we can cancel the radical sign since the x is raised by 2. so if you are going to simplify the given it will look like this,
x = √x^2
x = (x^2)^1/2
x = x
so it means, what ever the value is your x, it will satisfy the given inequality. :D

You are correct we can cancel square with square root, but it can be only apply when x is positive integer, in the case with x is negative it cannot be applied.

In short sqrt(x^2) = |x|