algebra help please...?

Question

if x is a real number such that x^4 + 2x^2 - 2x < 0, then 0
anyone knows how to prove this?


thanks

Answer 1

x(x^3+2x-2)
If x<0 then x^3+2x-2 is also less than 0 which means that x(x^3+2x-2) is positive, which we don't want.

If x>=1 then x^3+2x-2 >= 1+2-2 = 1 so x(x^3+2x-2) is again positive.

So the only possibility is 0

Answer 2

First, rewrite it as:

(1) x^2(x^2 + 2) < 2x

Now divide by x.Remember, however, that if an inequality is multiplied or divided by a negative number, the direction of the inequality changes, i.e. if a < b, and if c<0, then ac > ab. Furthermore, we cannot divide by x when x=0, so we have three different scenarios:

when x=0, x^4 + 2x^2 - 2x = 0, which does not satisfy the inequality. So x cannot be zero.


when x>0 , dividing (1) by x gives:

x(x^2 + 2) < 2

since x^2 is always > 0, (x^2 + 2) is always greater than 2.Therefore, x must be less than 1 if x(x^2 + 2) is to be less than 2.

when x < 0, division of (1) by x yields (remember to change the direction of the inequality)

x(x^2+2) > 2

since x^2 + 2 is always positive, it cannot be multiplied by a negative number to yield a product greater than 2. Thus x cannot be negative.

To recap: x cannot be zero
x must be less than 1
x cannot be negative

This means 0

Answer 3

just read your your book