Question

aratati ca nr a este patrat perfect si apoi calculati radical din a :
a = 2 x ( 1+2+3+ ... + 99) -99

Answer 1

a=2·(1+2+3+...+99)-99
a=2·(99·100:2)-99
a= 99·100-99
Daca dam factor comun 99 obtinem:
a=99·(100-1)
a=99·99
a=99²

Answer 2

$\displaystyle 2 \cdot (1+2+3+...+99)-99=2 \cdot \frac{99(99+1)}{2} -99= \\ \\ =2 \cdot \frac{99 \cdot 100}{2} -99=\not 2 \cdot \frac{9900}{\not 2} -99=9900-99= \\ \\ =99(100-1)=99 \cdot 99=99^2-p.p \\ \boxed{a=99^2-p.p} \\ \sqrt{a}=\sqrt{99^2}=99$