If A is the solution set of x^2 – 5x + 6 = 0 and B is the solution set of x - √(3x - 6) = 2, then A ∩ B =
If A is the solution set of x2 – 5x + 6 = 0 and B is the solution set of x - \(\sqrt{3x-6}\) = 2, then A ∩ B =
A) Φ
B) A
C) B
D) {2}
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Correct option is (D) {2}
\(x^2-5x+6=0\)
\(\Rightarrow\) (x - 2) (x - 3) = 0
\(\Rightarrow\) x - 2 = 0 or x - 3 = 0
\(\Rightarrow\) x = 2 or x = 3
\(\therefore\) A = {2, 3}
And \(x-\sqrt{3x-6}=2\)
\(\Rightarrow\) \(\sqrt{3x-6}=x-2\)
\(\Rightarrow3x-6=(x-2)^2\) (By squaring both sides)
\(\Rightarrow3x-6=x^2-4x+4\)
\(\Rightarrow x^2-7x+10=0\)
\(\Rightarrow\) (x - 2) (x - 5) = 0
\(\Rightarrow\) x = 2 or x = 5
\(\therefore\) B = {2, 5}
Now, \(A\cap B=\{2,3\}\cap\{2,5\}\) = {2}
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