Giúp mình bài này với, cảm ơn ạ

a)

$\left\{{{u_2=3}\atop{u_4=7}}\right.$

$⇔\left\{{{u_1+d=3}\atop{u_1+3d=7}}\right.$

$⇔\left\{{{u_1=1}\atop{d=2}}\right.$

$⇒$ Các số hạng là: $1; 3; 5; 7; 9$

b)

Gọi ba số lần lượt là $a, b, c, d$

$⇒\left\{\begin{array}{1}a+c=2b\\\hspace{0,5cm}bd=c^2\\a+d=21\\b+c=18\end{array}\right.$

$⇔\left\{\begin{array}{1}a=2b-c\\\hspace{0,5cm}bd=c^2\\2b-c+d=21\\b+c=18\end{array}\right.$

$⇔\left\{\begin{array}{}a=2b-c\\\hspace{0,5cm}bd=c^2\\c=2b+d-21\\3b+d=39\end{array}\right.$

$⇔\left\{\begin{array}{}a=2b-c\\\hspace{0,5cm}bd=c^2\\c=2b+d-21\\d=39-3b\end{array}\right.$

$⇔\left\{\begin{array}{}a=2b-c\\\hspace{0,5cm}bd=c^2\\c=18-b\\d=39-3b\end{array}\right.$

$⇔\left\{\begin{array}{}a=2b-c\\b(39-3b)=(18-b)^2\\c=18-b\\d=39-3b\end{array}\right.$

$⇔\left\{\begin{array}{}a=2b-c\\39b-3b^2=b^2-36b+324\\c=18-b\\d=39-3b\end{array}\right.$

$⇔\left\{\begin{array}{}a=2b-c\\\left[\begin{array}{}b=12\\b=6,75\end{array}\right.\\c=18-b\\d=39-3b\end{array}\right.$

Với $b=12 ⇒c=6; d=3; a=18$

$⇒$Dãy số cần tìm là: $18, 12, 6, 3$

Với $b=6,75 ⇒c=11,25; d=18,75; a=2,25$

$⇒$Dãy số cần tìm là: $2,25; 6,75; 11,25; 18,75$

c)

$\left\{\begin{array}{}u_7+u_15=60\\u_4^2+u_12^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1+6d+u_1+14d=60\\(u_1+3d)^2+(u_1+11d)^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1+10d=30\\u_1^2+6u_1d+9d^2+u_1^2+22u_1d+121d^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1=30-10d\\2u_1^2+28u_1d+130d^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1=30-10d\\2(30-10d)^2+28(30-10d)d+130d^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1=30-10d\\2(100d^2-600d+900)+840d-280d^2+130d^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1=30-10d\\200d^2-1200d+1800+840d-280d^2+130d^2=1170\end{array}\right.$

$⇔\left\{\begin{array}{}u_1=30-10d\\\left[\begin{array}{}d=3\\d=4,2\end{array}\right.\end{array}\right.$

Với $d=3 ⇒u_1=0$

Với $d=4,2 ⇒u_1=-12$

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