Question

помогите пж пж пж
$\frac{1}{11 - 2 \sqrt{30} } - \frac{1}{11 + 2 \sqrt{30} }$
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Answer 1

$\dfrac{1}{11 - 2 \sqrt{30} } - \dfrac{1}{11 + 2 \sqrt{30} } =$

$=\dfrac{11 + 2 \sqrt{30}}{(11 - 2 \sqrt{30})(11 + 2 \sqrt{30}) } - \dfrac{11 - 2 \sqrt{30}}{(11 - 2 \sqrt{30})(11 + 2 \sqrt{30}) } =$

$=\dfrac{11 + 2 \sqrt{30}-(11 - 2 \sqrt{30})}{(11 - 2 \sqrt{30})(11 + 2 \sqrt{30}) } =\dfrac{11 + 2 \sqrt{30}-11 + 2 \sqrt{30}}{11^2 - (2 \sqrt{30})^2 }$

$=\dfrac{4 \sqrt{30} }{121 - 2^2\cdot30 }=\dfrac{4 \sqrt{30} }{121 - 120 } =\dfrac{4 \sqrt{30} }{1 } =4 \sqrt{30}$