If x 3 - sqrt 3 find x2 frac 36 x 2 - JAMB Mathematics 1992 Question
If x = 3 - \(\sqrt{3}\), find x2 + \(\frac{36}{x^2}\)
A
9
B
18
C
24
D
27
correct option: c
x = 3 - (\sqrt{3})
x2 = (3 - (\sqrt{3}))2
= 9 + 3 - 6(\sqrt{34})
= 12 - 6(\sqrt{3})
= 6(2 - (\sqrt{3}))
∴ x2 + (\frac{36}{x^2}) = 6(2 - (\sqrt{3})) + (\frac{36}{6(2 - \sqrt{3})})
6(2 - (\sqrt{3})) + (\frac{6}{2 - \sqrt{3}}) = 6(- (\sqrt{3})) + (\frac{6(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})})
= 6(2 - (\sqrt{3})) + (\frac{6(2 + \sqrt{3})}{4 - 3})
6(2 - (\sqrt{3})) + 6(2 + (\sqrt{3})) = 12 + 12
= 24
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