What are the values of a and b.if any,where a|b-2|<0?
please some sugestions
a[b-2]< 0,
A positive number and a negative number of equal magnitude has equal absolute values. Therefore, we must solve 2 Eqs:
Eq1: a(b-2)< 0.
Eq2: a(-b+2) < 0.
a(b-2) < 0,
Divide both sides by a:
b-2 < 0,
b < 2.
a[b-2]< 0,
A positive number and a negative number of equal magnitude has equal absolute values. Therefore, we must solve 2 Eqs:
Eq1: a(b-2)< 0.
Eq2: a(-b+2) < 0.
Eq1: a(b-2) < 0,
Divide both sides by a:
b-2 < 0,
b < 2.
Divide both sides by (b-2):
a < 0.
Solution Set: b < 2, and a < 0.
Eq2: a(-b+2) < 0.
Divide both sides by a:
-b + 2 < 0,
-b < -2,
b > 2.
Divide both sides by (-b+2):
a < 0.
Solution set: b > 2, and a < 0.
To find the values of a and b where a|b-2| < 0, we need to consider the absolute value and the inequality.
However, it is important to note that the absolute value of any expression is always non-negative. In other words, |x| ≥ 0 for any real number x. Therefore, it is not possible for a|b-2| to be less than 0.
Hence, there are no values of a and b that satisfy the condition a|b-2| < 0.