aratati ca a=(1+2+3+...+50)-25x4 este patrat perfect si calculati radical din a
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Răspuns :

Salutare!

[tex]\bf a=(1+2+3+...+50)-25\cdot4[/tex]

[tex]\bf a=\dfrac{(50+1)\cdot 50}{2} -25\cdot4[/tex]

[tex]\bf a=\dfrac{51\cdot 50}{2} -100[/tex]

[tex]\bf a=\dfrac{51\cdot \not50}{\not 2} -100[/tex]

[tex]\bf a=\dfrac{51\cdot 25}{1} -100[/tex]

[tex]\bf a=51\cdot 25 -100[/tex]

[tex]\bf a=1275 -100[/tex]

[tex]\bf a=1175[/tex]

[tex]\bf a=5^{2} \cdot 47\implies \text{\bf nu este patrat perfect}[/tex]

[tex]\bf a=\sqrt{5^{2} \cdot 47} \implies \boxed{\bf a= 5\sqrt{47} }[/tex]

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