已知a>0且a≠1,设f(x)=a的x次方除以(a的x次方+根号a),求f(1/10)+f(2/10)+…+f(9/10)的值.作业本上的= = 还有一题是 (1+2的﹣1/6)(1+2的﹣1/4)(1+2的﹣1/2)=?解题步骤最好清晰一点,太乱了看不清 = =
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![已知a>0且a≠1,设f(x)=a的x次方除以(a的x次方+根号a),求f(1/10)+f(2/10)+…+f(9/10)的值.作业本上的= = 还有一题是 (1+2的﹣1/6)(1+2的﹣1/4)(1+2的﹣1/2)=?解题步骤最好清晰一点,太乱了看不清 = =](/uploads/image/z/570450-66-0.jpg?t=%E5%B7%B2%E7%9F%A5a%3E0%E4%B8%94a%E2%89%A01%2C%E8%AE%BEf%28x%29%3Da%E7%9A%84x%E6%AC%A1%E6%96%B9%E9%99%A4%E4%BB%A5%EF%BC%88a%E7%9A%84x%E6%AC%A1%E6%96%B9%2B%E6%A0%B9%E5%8F%B7a%EF%BC%89%2C%E6%B1%82f%EF%BC%881%2F10%29%2Bf%282%2F10%29%2B%E2%80%A6%2Bf%289%2F10%29%E7%9A%84%E5%80%BC.%E4%BD%9C%E4%B8%9A%E6%9C%AC%E4%B8%8A%E7%9A%84%3D+%3D+%E8%BF%98%E6%9C%89%E4%B8%80%E9%A2%98%E6%98%AF+%EF%BC%881%2B2%E7%9A%84%EF%B9%A31%2F6%29%281%2B2%E7%9A%84%EF%B9%A31%2F4%EF%BC%89%EF%BC%881%2B2%E7%9A%84%EF%B9%A31%2F2%EF%BC%89%3D%3F%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4%E6%9C%80%E5%A5%BD%E6%B8%85%E6%99%B0%E4%B8%80%E7%82%B9%2C%E5%A4%AA%E4%B9%B1%E4%BA%86%E7%9C%8B%E4%B8%8D%E6%B8%85+%3D+%3D)
已知a>0且a≠1,设f(x)=a的x次方除以(a的x次方+根号a),求f(1/10)+f(2/10)+…+f(9/10)的值.作业本上的= = 还有一题是 (1+2的﹣1/6)(1+2的﹣1/4)(1+2的﹣1/2)=?解题步骤最好清晰一点,太乱了看不清 = =
已知a>0且a≠1,设f(x)=a的x次方除以(a的x次方+根号a),求f(1/10)+f(2/10)+…+f(9/10)的值.
作业本上的= = 还有一题是 (1+2的﹣1/6)(1+2的﹣1/4)(1+2的﹣1/2)=?解题步骤最好清晰一点,太乱了看不清 = =
已知a>0且a≠1,设f(x)=a的x次方除以(a的x次方+根号a),求f(1/10)+f(2/10)+…+f(9/10)的值.作业本上的= = 还有一题是 (1+2的﹣1/6)(1+2的﹣1/4)(1+2的﹣1/2)=?解题步骤最好清晰一点,太乱了看不清 = =
f(1/10)+f(9/10)=(a^0.1)/(a^0.1+a^(1/2))+(a^0.9)/(a^0.9+a^(1/2))
通分:=【(a^0.1)*0.9+a^(1/2)+(a^0.9)*0.1+a^(1/2)】/【(a^0.1+a^(1/2))*(a^0.9+a^(1/2))】
=1
同理 f(2/10)+f(8/10)=1,f(3/10)+f(7/10)=1,f(4/10)+f(6/10)=1,f(5/10)+f(5/10)=1
所以 f(2/10)+f(8/10)+f(3/10)+f(7/10)+f(4/10)+f(6/10)+f(5/10)+f(1/10)+f(9/10)=4.5
很多年没做数学题了,这种数学技巧很强的题目我也爱莫能助,不好意思。
f(x)+f(1-x)
=a^x/(a^x+√a)+a^(1-x)/(a^(1-x)+√a)
=a^x[a^(1-x)+√a]+a^(1-x)(a^x+√a)/(a^x+√a)(a^(1-x)+√a)
=[a+a^x√a+a+a^(1-x)√a]/[a+a^x√a+a^(1-x)√a+a)
=1
∴f(1/10)+f(9/10)=f(2/10)+f(8/10...
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f(x)+f(1-x)
=a^x/(a^x+√a)+a^(1-x)/(a^(1-x)+√a)
=a^x[a^(1-x)+√a]+a^(1-x)(a^x+√a)/(a^x+√a)(a^(1-x)+√a)
=[a+a^x√a+a+a^(1-x)√a]/[a+a^x√a+a^(1-x)√a+a)
=1
∴f(1/10)+f(9/10)=f(2/10)+f(8/10)=...=2f(5/10)=1
∴f(1/10)+f(2/10)+……+f(9/10)
=[f(1/10)+f(9/10)]+[f(2/10)+f(8/10)]+...+f(5/10)
=4+1/2=4.5
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