Question

Calculati media aritmetica a numerelor reale x si y in urmatoarele cazuri:
a)
$3 \sqrt{8} - \sqrt{75} + 2 \sqrt{80} si \: y = \sqrt{32 } + 5 \sqrt{27} + 3 \sqrt{20 }$
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Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it x=3\sqrt8-\sqrt{75}+2\sqrt{80}=3\sqrt{4\cdot2}-\sqrt{25\cdot3}+2\sqrt{16\cdot5}=6\sqrt2-5\sqrt3+8\sqrt5\\ \\ \\ y=\sqrt{32}+5\sqrt{27}+3\sqrt{20}=\sqrt{16\cdot2}+5\sqrt{9\cdot3}+3\sqrt{4\cdot5}=4\sqrt2+15\sqrt3+6\sqrt5$

$\it m_a=\dfrac{6\sqrt2-5\sqrt3+8\sqrt5+4\sqrt2+15\sqrt3+6\sqrt5}{2}=\dfrac{10\sqrt2+10\sqrt3+14\sqrt5}{2}=\\ \\ \\ =\dfrac{2(5\sqrt2+5\sqrt3+7\sqrt5)}{2}=5\sqrt2+5\sqrt3+7\sqrt5$