Stepwise
Start practisingPractise

JAMB 1992 · UME · Q7

If x=3−3x = 3 - \sqrt3, find x2+36x2x^2 + \dfrac{36}{x^2}.

Worked solution (try it first)
  1. Square xx: (3−3)2=9−63+3(3 - \sqrt3)^2 = 9 - 6\sqrt3 + 3, which is 12−6312 - 6\sqrt3.
  2. Then 3612−63=62−3\dfrac{36}{12 - 6\sqrt3} = \dfrac{6}{2 - \sqrt3}.
  3. Multiply the top and bottom by 2+32 + \sqrt3.
  4. The bottom becomes 4−3=14 - 3 = 1, so this is 12+6312 + 6\sqrt3.
  5. Add: (12−63)+(12+63)=24(12 - 6\sqrt3) + (12 + 6\sqrt3) = 24, option C.

Report a problem with this question