Question

Aratati ca X este un numar natural patrat perfect:

a) x= ( 1+2+3+...+98) +49
b) x=1+3+5+...+225

Calculati X si aratati ca este patratul unui numar natural dupa calculati radacina patrata.

a) x=2+4+6+...+684-324 la puterea a 2-a
d)x= 1+2+3+,,,+224+16*450

Answer 1

1.
a.
x=99*98/2+49=99*49+49=100*49=10^2*7^2=70^2
b.
x=225*226/2-2*(1+2+3+...+112)=
=225*113-2*113*112/2=
=225*113-113*111=
=113*(225-111)=
=113*113=
=113^2

Answer 2

a) x=98*99/2+49= 4851+49=4900= 70la 2 deci este patrat perfect
b) x= 1+1*2+1+2*2+1+...+2*212+1)= 1+2(1+2+3+.....+112)+112= 1+2/2(112*113)+112= 1+12656+112=12769= 113la 2 este patrat per