Question

\(\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)

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Answer 1

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A=(2-\(\sqrt{3}\))\(\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)

8A=\(\left(4-2\sqrt{3}\right)\sqrt{52+30\sqrt{3}}-\left(4+2\sqrt{3}\right)\sqrt{52-30\sqrt{3}}\)

=\(\left(4-2\sqrt{3}\right)\sqrt{\left(3\sqrt{3}+5\right)^2}-\left(4+2\sqrt{3}\right)\sqrt{\left(3\sqrt{3}-5\right)^2}\)

=\(\left(4-2\sqrt{3}\right)\left(3\sqrt{3}+5\right)-\left(4+2\sqrt{3}\right)\left(3\sqrt{3}-5\right)\)

=12\(\sqrt{3}+20-18-10\sqrt{3}-12\sqrt{3}+20-18+10\sqrt{3}\)

=40-36

=4

\(\Rightarrow8A=4\Rightarrow A=\dfrac{1}{2}\)