Question

С решением и обьяснением :)
ответ: 6
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Answer 1

$((4+15^{0,5})^{0,5}-(4-15^{0,5})^{0,5})^{2}=\\\\=[(4+15^{0,5})^{0,5}]^{2}-2\cdot (4+15^{0,5})^{0,5} \cdot (4-15^{0,5})^{0,5}+[(4-15^{0,5})^{0,5}]^{2}=\\\\=4+15^{0,5} -2\cdot\sqrt{4+15^{0,5} }\cdot \sqrt{4-15^{0,5} }+4-15^{0,5}=\\\\=8-2\cdot \sqrt{4^{2} -(15^{0,5})^{2}}=8-2\sqrt{16-15}=8-2\cdot1=8-2=\boxed6$

Answer 2

ответ: $\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \huge \bold{} \boxed{6}$

Объяснение:

$\displaystyle\ \Large\ \boldsymbol{} \!\!\! 1) \ (a^{0,5} )^2=a^{0,5\cdot2} =a \\\\\\ 2) \ ( a+b)^2=a^2+2ab+b^2\\\\\\ ( \ (4+15^{0,5})^{0,5}-(4-15^{0,5})^{0,5} \ )^2= \\\\\\ (4+15^{0,5})^{0,5\cdot 2}-2 \cdot(4+15^{0,5})^{0,5} \cdot (4-15^{0,5})^{0,5}+(4-15^{0,5} )^{0,5\cdot2} \\\\\\ 4+\sqrt{15}\!\!\!\!\!\! \bigg{/}-2\cdot \sqrt{ 4^2-(\sqrt{15})^2 } +4-\sqrt{15}\!\!\!\!\!\! \bigg{/}= \\\\\\ 4+4-2\underbrace{\sqrt{16-15}}_1=8-2=\boxed{\bold6}$