Đáp án:
Giải thích các bước giải:
$1+2+3+...+x=120$ (ĐK: $n>0$)
$(x+1).\dfrac{(x-1):1+1}{2}=120$
$⇒(x+1).\dfrac{x}{2}=120$
$⇒\dfrac{x(x+1)}{2}=120$
$⇒x(x+1)=240$
$⇒x^{2}+x=240$
$⇒x^{2}+2x\dfrac{1}{2}+\dfrac{1}{4}=240+\dfrac{1}{4}$
$⇒(x+\dfrac{1}{2})^{2}=\dfrac{961}{4}$
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$⇒$\(\left[ \begin{array}{l}x+\frac{1}{2}=\frac{31}{2}\\x+\frac{1}{2}=\frac{-31}{2}\end{array} \right.\) ⇒\(\left[ \begin{array}{l}x=15(TM)\\x=-16(KTM)\end{array} \right.\)
$ $
Vậy $x=15$
