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\[\left| x^2 -1 \right| \le 4\]
Find the vlue of x
i got x is less than or equal to root 5 / x is greater than or equal to root negative 3
Could u give me a medal first plese
How do you do this question? O.o
Medal first please i onlybhelp ppl who give medals
Are meant to give medals first?
no u answer first then get medals -_______________-
Ok so u know absolute value is always positive right?
The number is not necessarily positive, but the definition is the value by which the number is farthest from zero (distance). Eg 1 and -1 both are 1 unit away from zero. That is why it is represented as a positive number. Also, distance can't be represented as a negative number. (e.g. You can't be -5 km away from home.)
|x² - 1| ≤ 4 -4 ≤ x² - 1 ≤ 4 -4 + 1 ≤ x² ≤ 4 + 1 -3 ≤ x² ≤ 5 √3 i ≤ x ≤ √5
Since √3i does not represent distance, the solution should only be written as x ≤ √5
what about minus root five?
There is no minus root 5
"There is actually no such thing as a plus-or-minus square root: it is merely language used to save words. For example, the equation x²=9 has two solutions, which are x=3 and x=-3. It is tedious to say: “since x²=9, x must be 3 or -3″. As a shortcut, we say: “since x²=9, x must be ±3.” http://www.xamuel.com/plus-or-minus-square-roots/
|x² - 1| ≤ 4 -4 ≤ x² - 1 ≤ 4 -4 + 1 ≤ x² ≤ 4 + 1 -3 ≤ x² ≤ 5 -√5 ≤ x ≤ √5
That should be it
|x² - 1| ≤ 4 x²≤ 4+1 x²≤5 √x²≤√5 x≤√5