(1/2)已知有理数a b c 满足la-1l+(b+3)的平方+(3c-1)2n次方=O(n为正整数)求(abc)125次方/(a9次方b3次
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![(1/2)已知有理数a b c 满足la-1l+(b+3)的平方+(3c-1)2n次方=O(n为正整数)求(abc)125次方/(a9次方b3次](/uploads/image/z/970861-13-1.jpg?t=%281%2F2%29%E5%B7%B2%E7%9F%A5%E6%9C%89%E7%90%86%E6%95%B0a+b+c+%E6%BB%A1%E8%B6%B3la-1l%2B%28b%2B3%29%E7%9A%84%E5%B9%B3%E6%96%B9%2B%283c-1%292n%E6%AC%A1%E6%96%B9%3DO%28n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%29%E6%B1%82%28abc%29125%E6%AC%A1%E6%96%B9%2F%28a9%E6%AC%A1%E6%96%B9b3%E6%AC%A1)
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(1/2)已知有理数a b c 满足la-1l+(b+3)的平方+(3c-1)2n次方=O(n为正整数)求(abc)125次方/(a9次方b3次
(1/2)已知有理数a b c 满足la-1l+(b+3)的平方+(3c-1)2n次方=O(n为正整数)求(abc)125次方/(a9次方b3次
(1/2)已知有理数a b c 满足la-1l+(b+3)的平方+(3c-1)2n次方=O(n为正整数)求(abc)125次方/(a9次方b3次
la-1l+(b+3)的平方+(3c-1)2n次方=O
a-1=0
b+3=0
3c-1=0
a=1
b=-3
c=1/3
(abc)^125
=(-3*1*1/3)^125
=(-1)^125
=-1
a^9b^3c^2
=1^9*(-3)^3*(1/3)^2
=1*(-27)*1/9
=-3
la-1l+(b+3)^2+(3c-1)2n次方=0
a-1=0 a=1
b+3=0 b=-3
3c-1=0 c=1/3
(abc)125次方/(a9次方b3次方)
=【1×(-3)×1/3】^125/【1^9×(-3)^3】
=【-1】^125/【1×(-27)】
=-1/(-27)
=1/27
由题意a-1=0且b+3=0且3c-1=0,故a=1,b=-3,c=1/3
(abc)125次方/(a9次方b3次=(-1)125次方/(1的9次方-3的3次方=-1/-27=1/27