Răspuns :

Loredanaschneidid

x²-2x+1+x²-4x+2²+...+x²-200x+100²= x²+2x+1+x²+4x+2²+...+x²+200x+100²

100x²-2x (1+2+3+...+100)+ 1²+2²+...+100²= 100x²+2x (1+2+3+...+100) + 1²+2²+...+100² |-100x²-(1²+2²+...+100²)

-2x(1+2+3+...+100)= 2x(1+2+3+...+100) |:2(1+2+...+100)

-x=x => x=0

Raspuns: x=0
  • (x  - 1)² + (x - 2)² + .. + (x - 100)² = (x + 1)² + (x + 2)² + .. + (x + 100)²
  • (x² - 2x + 1²) + (x² - 4x + 2²) + .. + (x² - 200x + 100²) = (x² + 2x + 1²) + (x² + 4x + 2²) + .. + (x² + 200x + 100²)
  • 100x² - 2x(1 + 2 + .. + 100) + (1² + 2² + 100²) = 100x² + 2x(1 + 2 + .. +100) + (1² + 2² + .. + 100²)
  • 100x² - 100x² - 2x·5050 - 2x·5050 + (1² + 2² + .. + 100²) - (1² + 2² + .. + 100²) = 0
  • - 10100x - 10100x = 0
  • - 20200x = 0
  • x = 0