x^2-5x+6/(x-4)>0 then x € = ____
Answers
EXPLANATION.
⇒ x² - 5x + 6/(x - 4) > 0.
As we know that,
First Factorizes the numerator, we get.
⇒ x² - 5x + 6.
Factorizes the equation into middle term splits, we get.
⇒ x² - 3x - 2x + 6.
⇒ x(x - 3) - 2(x - 3).
⇒ (x - 2)(x - 3).
Now, we can write equation as,
⇒ (x - 2)(x - 3)/(x - 4) > 0.
First find the zeroes of the equation, we get.
⇒ x - 2 = 0.
⇒ x = 2. - - - - - (1).
⇒ x - 3 = 0.
⇒ x = 3. - - - - - (2).
⇒ x - 4 = 0.
⇒ x = 4. - - - - - (3).
Put this point on wavy curve method, we get.
⇒ x ∈ (2,3) ∪ (4,∞).
MORE INFORMATION.
Number of elements in different sets.
If A, B & C are finite sets and U be the finite universal set, then.
(1) = n(A ∪ B) = n(A) + n(B) - n(A ∩ B).
(2) = n(A ∪ B) = n(A) + n(B) (if A & B are disjoint sets).
(3) = n(A - B) = n(A) - n(A ∩ B).
(4) = n(A Δ B) = n[(A - B) ∪ (B - A)] = n(A) + n(B) - 2n(A ∩ B).
(5) = n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C).
(6) = n(A' ∪ B') = n(A ∩ B)' = n(U) - n(A ∩ B).
(7) = n(A' ∩ B') = n(A ∪ B)' = n(U) - n(A ∪ B).