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受欢迎的代数 >

展开 (-5+sqrt(61))^6

解答

展开

(- 5 + 61)^{6}

解答

2209856 - 28288061

+1

十进制

492.57167 \dots

求解步骤

(- 5 + 61)^{6}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = - 5, b = 61

= i = 0 \sum 6 (i 6) (- 5)^{(6 - i)} (61)^{i}

展开求和

= \frac{6 !}{0 ! ( 6 - 0 ) !} (- 5)^{6} (61)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (- 5)^{5} (61)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (- 5)^{4} (61)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (- 5)^{3} (61)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (- 5)^{2} (61)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (- 5)^{1} (61)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (- 5)^{0} (61)^{6}

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} (- 5)^{6} (61)^{0} : 15625

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} (- 5)^{5} (61)^{1} : - 1875061

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} (- 5)^{4} (61)^{2} : 571875

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} (- 5)^{3} (61)^{3} : - 15250061

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} (- 5)^{2} (61)^{4} : 1395375

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} (- 5)^{1} (61)^{5} : - 11163061

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} (- 5)^{0} (61)^{6} : 226981

= 15625 - 1875061 + 571875 - 15250061 + 1395375 - 11163061 + 226981

15625 - 1875061 + 571875 - 15250061 + 1395375 - 11163061 + 226981 = 2209856 - 28288061

= 2209856 - 28288061

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