1) x^2 > 2
how can we get the following solution ?
x < - sqrt(2) < -1 or x > sqrt(2) > 1
x^2 > 2
take the sqrt
x > sqrt(2) or x < - sqrt(2). and - sqrt(2) is less than -1.
take any value. lets say x^2 = 25. x can either be 5 or smaller than -5.
x (5) > sqrt (2).
x (-5) < - sqrt (2).
2) x^2 > x
how to derive the solution for x ?
x^2 > x
x^2 - x > 0
x (x- 1) > 0
here it ios correct to say x > 1 but not x>0. actually x>1 but is <0.
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3) What does the following mean for a triangle
AC^2 + AB^2 > BC^2
this means the triangle is not a right triangle.