Question

Ex2 Aratati ca numarul x este un patrat perfect

b)×=1+3+5+.........+101
h) ×=243 la puterea 2 -(240la puterea 2 +3•240)


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Answer 1

b)×=1+3+5+.........+101=

1+2+3+...100+101-(2+4+6+...+100)=

1+2+3+...100+101-2(1+2+3+...50)=

101×102/2-2×50×51/2=51×101-50×51=

51(101-50)=51×51=51²

h) ×=243² -(240² +3•240)=

243²-240²-3×240=

(243-240)(243+240)-3×240=

3×(243+240)-3×240=

3×243+3×240-3×240=

=729=27²