[กิตติ]

ข้อความเดิมเขียนโดยคุณ ครูนะ

1. กำหนดระบบสมการ

$X_{1} + 4X_{2} + 9X_{3} + 16X_{4} + 25X_{5} + 36X_{6} + 49X_{7} = 3$

$4X_{1} + 9X_{2} + 16X_{3} + 25X_{4} + 36X_{5} + 49X_{6} + 64X_{7} = 23$

$9X_{1} + 16X_{2} + 25X_{3} + 36X_{4} + 49X_{5} + 64X_{6} + 81X_{7} = 234$

จงหาค่าของ

$16X_{1} + 25X_{2} + 36X_{3} + 49X_{4} + 64X_{5} + 81X_{6} + 100X_{7}$

ข้อ1...ผมคุ้นๆว่าเคยทำแล้ว

$16X_{1} + 25X_{2} + 36X_{3} + 49X_{4} + 64X_{5} + 81X_{6} + 100X_{7}$
$=\left(\,9X_{1} + 16X_{2} + 25X_{3} + 36X_{4} + 49X_{5} + 64X_{6} + 81X_{7} \right)+ $
$7X_{1}+9X_{2} + 11X_{3} + 13X_{4} + 15X_{5} + 17X_{6} + 19X_{7}$

$X_{1} + 4X_{2} + 9X_{3} + 16X_{4} + 25X_{5} + 36X_{6} + 49X_{7} = 3$...(1)

$4X_{1} + 9X_{2} + 16X_{3} + 25X_{4} + 36X_{5} + 49X_{6} + 64X_{7} = 23$...(2)

$9X_{1} + 16X_{2} + 25X_{3} + 36X_{4} + 49X_{5} + 64X_{6} + 81X_{7} = 234$...(3)

(2)-(1) $3X_{1} + 5X_{2} + 7X_{3} + 9X_{4} + 11X_{5} + 13X_{6} + 15X_{7} = 20$...(4)

(3)-(2) $5X_{1} + 7X_{2} + 9X_{3} + 11X_{4} + 13X_{5} + 15X_{6} + 17X_{7} = 211$...(5)

(5)-(4) $2X_{1} + 2X_{2} + 2X_{3} + 2X_{4} + 2X_{5} + 2X_{6} + 2X_{7} = 191$....(6)

(5)+(6) $7X_{1}+9X_{2} + 11X_{3} + 13X_{4} + 15X_{5} + 17X_{6} + 19X_{7}=402$

$16X_{1} + 25X_{2} + 36X_{3} + 49X_{4} + 64X_{5} + 81X_{6} + 100X_{7}$
$=234+402=636 $