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Prin progresie aritmetica rezolvati in mulţimea nr.reale ecuatia:
x+2x+3x+4x+...+x la puterea a doua=288


Răspuns :

x+2x+3x+4x+...+x²=288
x(1+2+3+4+...+x)=288
x*x*(x+1):2=288
x²(x+1)=2*288
x²(x+1)=576
stim ca 8³=512<x²(x+1)<9³=729
=> x=8 si avem 8²*9=576 verifica!