Đáp án:
1. y=17
2.x=13
Giải thích các bước giải:
1. \(\begin{array}{l}
C_{y + 8}^{y + 3} = 5.A_{y + 6}^3(dk:y \ge - 3)\\
\leftrightarrow \frac{{(y + 8)!}}{{(y + 3)!(y + 8 - y - 3)!}} = 5.(y + 6)(y + 5)(y + 4)\\
\leftrightarrow \frac{{(y + 8)(y + 7)(y + 6)(y + 5)(y + 4)(y + 3)!}}{{(y + 3)!.5!}} = 5.(y + 6)(y + 5)(y + 4)\\
\leftrightarrow (y + 8)(y + 7)(y + 6)(y + 5)(y + 4) = 600(y + 6)(y + 5)(y + 4)\\
\leftrightarrow \left[ {(y + 8)(y + 7) - 600} \right](y + 6)(y + 5)(y + 4) = 0\\
\leftrightarrow ({y^2} + 15y - 544)(y + 6)(y + 5)(y + 4) = 0\\
\leftrightarrow \left[ \begin{array}{l}
y = 17(tm)\\
y = - 32(l)\\
y = - 6(l)\\
y = - 5(l)\\
y = - 4(l)
\end{array} \right. \leftrightarrow y = 17\\
\end{array}\)
2. \(\begin{array}{l}
3C_x^3 + A_{x + 1}^2 = 1040(dk:x \ge 3)\\
\leftrightarrow 3.\frac{{x(x - 1)(x - 2)}}{{3!}} + (x + 1).x = 1040\\
\leftrightarrow x(x - 1)(x - 2) + 2(x + 1)x = 2080\\
\leftrightarrow {x^3} - 2{x^2} - {x^2} + 2x + 2{x^2} + 2x = 2080\\
\leftrightarrow {x^3} - {x^2} + 4x - 2080 = 0\\
\leftrightarrow x = 13(tm)
\end{array}\)
