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If \(\frac {3 - \sqrt 3}{2 + \sqrt 3} = a + b\sqrt...

If 332+3=a+b3, what are the values a and b?

A.

a = 9, b = -5

B.

a = 5, b = 9

C.

a = 9, b = 5

D.

a = -5, b = 9

Correct answer is A

332+3=a+b3

Rationalize

= 332+3×2323

= (33)(2+3)(23)(23)

= 63323+(3)2423+23(3)2

= 653+343

= 9531=953

= 9 + (-5) 3