Prelim. Questions (1 Viewer)

[GaDaMIt]

For which values of x is the following true:

1) x multiplied by x < (greater than or equal to) x + x

and likewise..

2) x times x times x < (greater than or equal to) x + x + x

I know the answers to both but I don't understand the algebraic method for obtaining the answers. Please give full working and maybe explain it.

Those 2 questions are from the Cambridge year 11 3u maths textbook. Exercise 1A Question 18 - The extension question.

 

[Mountain.Dew]

For which values of x is the following true:

1) x multiplied by x < (greater than or equal to) x + x

and likewise..

2) x times x times x < (greater than or equal to) x + x + x

I know the answers to both but I don't understand the algebraic method for obtaining the answers. Please give full working and maybe explain it.

Those 2 questions are from the Cambridge year 11 3u maths textbook. Exercise 1A Question 18 - The extension question.

1) we have x² <= 2x

so, x² - 2x <= 0

x(x-2) <= 0

therefore, critical pts are 0, 2.

draw the graph of y = x(x-2), and have a look at the graph where the curve is below the x-axis. the x-values that obtain those negative values is ur range of values of x's to satisfy the equation.

So, the solution IS ==> 0 <= x <= 2.

2) same procedure, x³ <= 3x
so x³ - 3x <= 0

x(x²-3) <= 0, x(x-sqrt3)(x+sqrt3) <=0

so critical pts are: x=0,sqrt3, -sqrt3.

same procedure ==> draw the graph of y= x(x-sqrt3)(x+sqrt3) and observe between what values of x its y value is negative. and u have u answer thus: -sqrt3 <= x <=0, x >= sqrt3.