有關國二數學乘法公式 1. (5+1)(5^2+1)(5^4+1)=5^8-1/k,求k=? 2. 若a-b=-3,ab=2,則2a^2-3ab+2b^2=?

1.
5^8-1 = (5⁴-1) (5⁴+1)
. . . . . = (5²-1) (5²+1) (5⁴+1)
. . . . . = (5-1) (5+1) (5²+1) (5⁴+1)
. . . . . = 4 (5+1) (5²+1) (5⁴+1)
∴ (5+1) (5²+1) (5⁴+1) = (5^8-1) /4

∴ k = 4

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2.
a-b = -3
(a-b)² = 9
a²-2ab+b² = 9
2a²-4ab+2b² = 18
(2a²-3ab+2b²) -ab = 18
(2a²-3ab+2b²) -2 = 18
∴ 2a²-3ab+2b² = 20

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註 :
==
題目 1.
-- 題目的原意是否應為： (5+1) (5²+1) (5⁴+1) = (5^8-1) /k ？
以上的解是用這 數式 來計算！

Sol
1
A=(5+1)(5^2+1)(5^4+1)
4A=4*(5+1)(5^2+1)(5^4+1)
=(5－1)(5+1)(5^2+1)(5^4+1)
=(5^2－1)(5^2+1)(5^4+1)
=(5^4－1)(5^4+1)
=5^8－1
k=1
2
Sol
a－b=，3
a^2+b^2，2ab=9
2a^2+2b^2，4ab=18
2a^2+2b^2，3ab=18+ab=20