Question

15 Arătaţi că numărul x este natural, unde:
X= V19/2,(1) + V20/ 2, (2) + V 21/2,(3) +...+ V 26/2,(8).​

Answer 1

Răspuns:

$\sqrt{\frac{19}{2,(1)} }=\sqrt{\frac{19}{\frac{21-2}{9} } } =\sqrt{\frac{19}{\frac{19}{9} } } =\sqrt{19:\frac{19}{9} }=\sqrt{19*\frac{9}{19} } =\sqrt{9} =3\\\sqrt{\frac{20}{2,(2)} }=\sqrt{\frac{20}{\frac{22-2}{9} } } =\sqrt{\frac{20}{\frac{20}{9} } } =\sqrt{20:\frac{20}{9} }=\sqrt{20*\frac{9}{20} } =\sqrt{9} =3\\\sqrt{\frac{21}{2,(3} }=\sqrt{\frac{21}{\frac{23-2}{9} } } =\sqrt{\frac{21}{\frac{21}{9} } } =\sqrt{21:\frac{21}{9} }=\sqrt{21*\frac{9}{21} } =\sqrt{9} =3$

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$\sqrt{\frac{26}{2,(8)} }=\sqrt{\frac{26}{\frac{28-2}{9} } } =\sqrt{\frac{26}{\frac{26}{9} } } =\sqrt{26:\frac{26}{9} }=\sqrt{26*\frac{9}{26} } =\sqrt{9} =3$

$\sqrt{\frac{19}{2,(1)} }+\sqrt{\frac{20}{2,(2)} }+\sqrt{\frac{21}{2,(3)} } +...+\sqrt{\frac{26}{2,(8)} } = 3+ 3+3 +..+ 3$

De la 19 la 26 sunt :26-19+1 = 8 numere Deci va fi 3+3+3+..+3 de 8 ori = 8*3=24

Explicație pas cu pas: