If a, b are real number, two sets \(\displaystyle \{1,a+b,a\}\) and \(\left\{0,\frac{b}{a},b\right\}\) What is b - a?
+23245 If the two sets are equal, that is, if they contain the same elements, then:
{1, a + b, a} and {0, b/a, b}
The '0' of the second set cannot equal a becuase that would make the expression b/a undefined.
So a + b = 0 ---> a = -b.
If 1 = b, then a = -1.
Let's see if this works:
The first set has: 1, a + b = -1 + 1 = 0, and a = -1.
The second set has: 0, b/a = 1/-1 = -1, and b = 1.
So, the first set does contain the same numbers as the second set.
Now, to find b - a = 1 - -1 = 1 + 1 = 2.
