​ If = (5 - √3)(2 + √3) = x + y √3 , then A. x = 13, y = - 7 B. x = -13, y = 7 C. x = -13, y = - 7 D. x = 13, y = 7 ​

Question

If = \(\frac{5-\sqrt3}{2+\sqrt3}\) = x + y √3 , then

A. x = 13, y = -7

B. x = -13, y = 7

C. x = -13, y = -7

D. x = 13, y = 7

Answer 1

\(\frac{5-\sqrt3}{2+\sqrt3}\) = x + y√3

= \(\frac{5-\sqrt3}{2+\sqrt3}\) × \(\frac{2-\sqrt3}{2-\sqrt3}\)

= \(\frac{(10-5\sqrt3-2\sqrt3+3)}{(4-3)}\)

= 10 – 7√3 +3

= 13 – 7√3 = x + y√3

So, x = 13 , y = - 7