Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

1/(2-√3)^2=？

A. 2+√3
B. 2-√3
C. 7+4√3
D. 7-4√3
E. 4+7√3

Nice problem!
\[? = \frac{1}{{{{\left( {2 - \sqrt 3 } \right)}^2}}} = \frac{1}{{{{\left( {2 - \sqrt 3 } \right)}^2}}} \cdot \frac{{{{\left( {2 + \sqrt 3 } \right)}^2}}}{{{{\left( {2 + \sqrt 3 } \right)}^2}}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{\left( {2 + \sqrt 3 } \right)^2} = 4 + 4\sqrt 3 + 3 = 7 + 4\sqrt 3 \]
\[\left( * \right)\,\,\,{\left( {2 - \sqrt 3 } \right)^2}{\left( {2 + \sqrt 3 } \right)^2} = {\left[ {\left( {2 - \sqrt 3 } \right)\left( {2 + \sqrt 3 } \right)} \right]^2} = {\left[ {{2^2} - {{\left( {\sqrt 3 } \right)}^2}} \right]^{\,2}} = 1\]

The correct answer is therefore [spoiler]__(C)____[/spoiler] .

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

=>

1/(2-√3)^2= [1/(2-√3)]^2= {(2+√3)/{(2-√3)(2+√3)}^2={(2+√3)/(4-3)}^2=(2+√3)^2= 4+4√3+3 = 7+4√3.

Therefore, the answer is C.
Answer: C