Question

Imi puteti rezolva aceasta ecuatie cu formula lui Gauss

Answer 1

Răspuns:

Explicație pas cu pas:

x + 2x +3x +....+100x=5049x-1

x (1+2+3+...100)=5049x-1

x*100*101/2 =5049x-1

5050x=5049x-1

5050x-5049x=-1

x=-1

Answer 2

$\it x+2x+3x+\ ...\ +100x = 5049x - 1 \Rightarrow x(1+2+3+\ ...\ +100)=5049x-1\Rightarrow\\ \\ \Rightarrow\ x\cdot\dfrac{100\cdot101}{2}-5049x=-1\Rightarrow x\cdot5050-5049x=-1 \Rightarrow\\ \\ \Rightarrow x(5050-5949)=-1 \Rightarrow x\cdot 1=-1 \Rightarrow x=-1$