Question

B)

Answer 1

Answer:

P + Q = 1

Step-by-step explanation:

Given: $\frac{1+\sqrt{3} }{1-\sqrt{3} }$  = P - $\sqrt{Q}$

This is a question on surd, so we need to rationalize the denominator to have;

$\frac{1+\sqrt{3} }{1-\sqrt{3} }$  * $\frac{1+\sqrt{3} }{1+\sqrt{3} }$ = $\frac{1+\sqrt{3}+\sqrt{3} + 3}{1+\sqrt{3}-\sqrt{3} -3 }$

   = $\frac{4+ 2\sqrt{3} }{1-3}$

   = $\frac{4+2\sqrt{3} }{-2}$

   = -2 - $\sqrt{3}$

Thus,

-2 - $\sqrt{3}$ = P - $\sqrt{Q}$

⇒ P = -2 and Q = 3

Therefore, the value of P + Q = -2 + 3

                                                 = 1

Thus,

P + Q = 1