Question

ajutor!! toate cele 3 puncte, si explicate, va rog!!
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Answer 1

$\displaystyle a)~\frac{5}{3\sqrt{2} }~si~\frac{7}{2\sqrt{3} } \\\\ \frac{5}{3\sqrt{2} } \rightarrow amplificam~fractia~cu~7:~\frac{^{7)}5}{3\sqrt{2} } =\frac{7 \cdot 5}{7 \cdot 3\sqrt{2} } =\frac{35}{21\sqrt{2} } \\\\ \frac{7}{2\sqrt{3} } \rightarrow amplificam~fractia~cu~5:~\frac{^{5)}7}{2\sqrt{3} } =\frac{5 \cdot 7}{5 \cdot 2\sqrt{3} }=\frac{35}{10\sqrt{3} }\\\\ \frac{5}{3\sqrt{2} } ~si~\frac{7}{2\sqrt{3} } \rightarrow \frac{35}{21\sqrt{2} } ~si~\frac{35}{10\sqrt{3} }$

$21\sqrt{2} \rightarrow introducem~factorii~sub~radical:\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~21\sqrt{2} =\sqrt{21^2\cdot2} =\sqrt{441*2} =\sqrt{882} \\\\ 10\sqrt{3} \rightarrow introducem~factorii~sub~radical:\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~10\sqrt{3} =\sqrt{10^2\cdot 3}=\sqrt{100\cdot 3} =\sqrt{300}$

$\displaystyle \frac{5}{3\sqrt{2} } ~si~\frac{7}{2\sqrt{3} } \rightarrow \frac{35}{21\sqrt{2} } ~si~\frac{35}{10\sqrt{3} } \rightarrow \frac{35}{\sqrt{882} } ~si~\frac{35}{\sqrt{300} } \\\\ 35=35;~\sqrt{882} > \sqrt{300} \Rightarrow \frac{5}{3\sqrt{2} } > \frac{7}{2\sqrt{3} }$

$b)~\sqrt{5^2-4^2} \cdot \sqrt{5^2\cdot 4^2} =\sqrt{25-16} \cdot \sqrt{25 \cdot 16}= \sqrt{9} \cdot \sqrt{400} =3 \cdot 20=60$

$\displaystyle c)~|0,4-1|+|0,4+2|\\\\ 0,4\rightarrow transformam~in~fractie~ordinara:~0,4=\frac{4}{10}$

$\displaystyle \underbrace{\Bigg|\frac{4}{10} -^{10)}1\Bigg|+\Bigg|\frac{4}{10}+^{10)}2\Bigg| }=\Bigg|\frac{4-10}{10} \Bigg|+\Bigg|\frac{4+20}{10}\Bigg|=\underbrace{\Bigg|-\frac{6}{10} \Bigg|+\Bigg|\frac{24}{10}\Bigg|} \\Amplificam~pe~1~si~pe~2~cu~10.~~~~~~~~~~~~~~~\underbrace{|a|=\left \{ {{opusul~lui~a~daca~a < 0} \atop {0~daca~a=0}} \atop{a~daca~a > 0}}\right. }\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~In~cazul~nostru,~-\frac{6}{10} < 0~si~\frac{24}{10} > 0,$

$\displaystyle \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~deci~\Bigg|-\frac{6}{10} \Bigg|=\frac{6}{10} ~si ~\Bigg|\frac{24}{10} \Bigg|=\frac{24}{10}$

$\displaystyle |0,4-1|+|0,4+2|=\frac{6}{10} +\frac{24}{10} =\frac{30}{10}=3$

Answer 2

Răspuns:

a) 7/(2√3)

b) 60

c) 3

Explicație pas cu pas:

a) 5/(3√2)   si 7/(2√3)

Aducem la acelasi numitor :

5/(3√2) = 5·2√3/(3√2·2√3) = 10√3/(6√6)

7/(2√3) = 7·3√2/(2√3·3√2) = 21√2/(6√6)

10√3 = √300 ;  21√2 = √882 =>

√882 > √300 => 7/(2√3) >  5/(3√2)

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b) √(5²-4²) ·√(5²·4²) = √(25-16) ·5·4 = √9·20 = 3·20 = 60

c) I0,4-1I + I0,4+2I = 1-0,4+0,4+2 = 1+2 = 3

1>0,4 =>  I0,4-1I = 1-0,4