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Surds and Indices

Q1:

If x = 3 + 22, then the value of x - 1 is:
x

A 1

B 2

C
22

D
33

ANS:B - 2

x - 1 2 = x + 1 - 2
x x
   = (3 + 22) + 1 - 2
(3 + 22)
   = (3 + 22) + 1 x (3 - 22) - 2
(3 + 22) (3 - 22)
   = (3 + 22) + (3 - 22) - 2    = 4.
x - 1 = 2.
x



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