Question

simplify part 6 pls help.

Answer 1

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Answer 2

Given Equation can be written as:

$\frac{1}{(2 - \sqrt{3})^3 } + \frac{1}{(2 + \sqrt{3})^3 }$

$\frac{(2 + \sqrt{3})^3 + (2 - \sqrt{3})^3 }{(2 + \sqrt{3})^3(2 - \sqrt{3})^3 }$

We know that (a+b)^3 = a^3+b^3+3a^2b + 3ab^2, (a-b)^3 = a^3-b^3 -3a^2b+3ab^2.

$\frac{2^3+(\sqrt{3} )^3+3*2^2 \sqrt{3} + 3*2( \sqrt{3})^2 + 2^3 - 3 * 2^2 * \sqrt{3} + 3 * 2( \sqrt{3})^2 - ( \sqrt{3})^3 }{(2 + \sqrt{3})^3 (2 - \sqrt{3} )^3 }$

$\frac{12 \sqrt{3} + 3 \sqrt{3}+ 8 + 18 + 8 + 18 - 15 \sqrt{3} }{676 - 675}$

$\frac{15 \sqrt{3} + 26 + 26 - 15 \sqrt{3} }{1}$

$\frac{52}{1}$

52.


Hope this helps!