If x = 2/3 + √7 then (x – 3)2 = ……………A) 1 B) 4 C) 3�

1.	If x = 2/3 + √7 then (x – 3)2 = ……………A) 1 B) 4 C) 3 D) 7
Answer» Correct option is (D) 7 \((x-3)^2\) \(=\left(\frac{2}{3+\sqrt7}-3\right)^2\) \(=\left(\frac{2-9-3\sqrt7}{3+\sqrt7}\right)^2\) \(=\left(\frac{-7-3\sqrt7}{3+\sqrt7}\right)^2\) \(=\frac{(7+3\sqrt7)^2}{(3+\sqrt7)^2}\) \(=\frac{(\sqrt7(\sqrt7+3))^2}{(3+\sqrt7)^2}\) \(=\frac{(\sqrt7)^2(3+\sqrt7)^2}{(3+\sqrt7)^2}\) = 7 Correct option is D) 7

If x = 2/3 + √7 then (x – 3)2 = ……………A) 1 B) 4 C) 3 D) 7

Answer»

Correct option is (D) 7

\((x-3)^2\) \(=\left(\frac{2}{3+\sqrt7}-3\right)^2\)

\(=\left(\frac{2-9-3\sqrt7}{3+\sqrt7}\right)^2\) \(=\left(\frac{-7-3\sqrt7}{3+\sqrt7}\right)^2\)

\(=\frac{(7+3\sqrt7)^2}{(3+\sqrt7)^2}\) \(=\frac{(\sqrt7(\sqrt7+3))^2}{(3+\sqrt7)^2}\)

\(=\frac{(\sqrt7)^2(3+\sqrt7)^2}{(3+\sqrt7)^2}\) = 7

Correct option is D) 7