Question

!!DAU COROANA!!
Se consideră mulțimea M={1,44;36/25;4/16;3 1/16;1,(7)}.Determinați elementele mulțimii P = { x | x = √ y , y ∈ M }.

Answer 1

Răspuns:

$P = \left\{\frac{6}{5};\,\frac{1}{2} ;\,\frac{7}{4};\,\frac{4}{3}\right\}$

Explicație pas cu pas:

$M = \left\{1.44;\,\frac{36}{25};\, \frac{4}{16};\,3 \frac{1}{6};\,1,(7)\right\}$

$P = \{x \,|\,x = \sqrt{y},\,\, y\in M\}$

Mulțimea P este formată din radicalii elementelor care aparțin mulțimii M.

$M = \left\{\frac{144}{100};\, \frac{36}{25};\, \frac{4}{16} ;\, \frac{3\cdot 16+1}{16};\, \frac{17-1}{9}\right\} = \left\{\frac{144}{100};\,\frac{36}{25};\, \frac{4}{16} ;\, \frac{49}{16};\,\frac{16}{9}\right\} =$

$= \left\{\left(\frac{12}{10}\right)^2;\, \left(\frac{6}{5}\right)^2;\, \left(\frac{2}{4}\right)^2;\, \left(\frac{7}{4}\right)^2;\, \left(\frac{4}{3}\right)^2\right\} =$

$= \left\{\left(\frac{6}{5}\right)^2;\, \left(\frac{1}{2}\right)^2;\, \left(\frac{7}{4}\right)^2;\, \left(\frac{4}{3}\right)^2\right\}$

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