Question

Tính:         
  600 - ( 1 + 3 + 5 +...+ x ) = 375

Answer 1

=>1+3+5+...+x=225

Số số hạng là (x-1):2+1

Tổng là: \(\dfrac{\dfrac{\left(x+1\right)\left(x-1\right)}{2}+1}{2}=\dfrac{x^2-1+2}{4}=\dfrac{x^2+1}{4}\)

=>\(\dfrac{x^2+1}{4}=225\)

\(\Leftrightarrow x^2+1=900\)

=>x²=899

hay \(x=\sqrt{899}\)

Answer 2

\(600-\left(1+3+5+...+x\right)=375\)

\(\Rightarrow\dfrac{\left(x-1\right):2+1}{2}\left(x+1\right)=225\)

\(\Rightarrow\dfrac{x+1}{4}\left(x+1\right)=225\)

\(\Rightarrow\left(x+1\right)^2=900\)

\(\Rightarrow x+1=30\left(x>0\right)\)

\(\Rightarrow x=29\)