Question

1+4+7+...+x=590 aflati x​

Answer 1

1 + 4 + 7 + ... + x = (1+x)*[(x-1)/3+1]/2 = 590

(1+x) * (x-1+3)/3 = 590*2 = 1180

(x+1)(x+2) = 1180*3 = 3540

x^2 + 2x+ x + 2 = 3540

x^2 + 3x - 3538 = 0

Delta = 9 + 4*3538 = 14161 = 7^2 * 17^2

x1 = -3 + radical(7^2*17^2)/2 = (-3+7*17)/2 = (-3+119)/2 = 116/2 = 58

x2 = -3 - radical(7^2*17^2)/2 = (-3-119)/2 = -122/2 = -61

Dar x>0 => solutia este x = 58