Let S , be the set of all real roots of the equation, 3 x 3 x - 1 + 2 = 3 x - 1 + 3 x - 2 , then
Let , be the set of all real roots of the equation, , then
contains exactly two elements.
is a singleton.
is an empty set.
contains at least four elements.
Solution
$3^x = t$
$t|t-1| + 2 = |t-1| + |t-2|$
$t^2 - t + 2 = |t-1| + |t-2|$
Let, $f(t) = t^2 - t + 2$ and $g(t) = |t-1| + |t-2|$
$f(t)$ and $g(t)$ has a solution at $t=a$
$3^x = a \Rightarrow x = \log_3 a$
So, it is a singleton set.
