数学
         
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    总述:本次共解1题。其中
           ☆方程1题

〖 1/1方程〗
    作业:求方程 20/(1+x)+20/((1+x)*(1+x))+20/((1+x)*(1+x)*(1+x))+20/((1+x)*(1+x)*(1+x)*(1+x))+220/((1+x)*(1+x)*(1+x)*(1+x)*(1+x)) = 100 的解.
    题型:方程
    解:原方程:
     20 ÷ (1 + x ) + 20 ÷ ((1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )) + 220 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) = 100
     方程两边同时乘以:(1 + x )
     20 + 20 ÷ ((1 + x )(1 + x )) × (1 + x ) + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x ) + 20 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )) × (1 + x ) + 220 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) = 100(1 + x )
    去掉方程左边的一个括号:
     20 + 20 ÷ ((1 + x )(1 + x )) × 1 + 20 ÷ ((1 + x )(1 + x )) × x + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x ) + 20 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )) = 100(1 + x )
    去掉方程右边的一个括号:
     20 + 20 ÷ ((1 + x )(1 + x )) × 1 + 20 ÷ ((1 + x )(1 + x )) × x + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x ) + 20 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )) = 100 × 1 + 100 x
    方程化简为:
     20 + 20 ÷ ((1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )) × x + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x ) + 20 ÷ ((1 + x )(1 + x )(1 + x )(1 + x )) × (1 + x ) = 100 + 100 x
     方程两边同时乘以:((1 + x )(1 + x ))
     20((1 + x )(1 + x )) + 20 + 20 ÷ ((1 + x )(1 + x )) × x ((1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x )((1 + x )(1 + x )) + 20 = 100((1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))
    去掉方程左边的一个括号:
     20(1 + x )(1 + x ) + 20 + 20 ÷ ((1 + x )(1 + x )) × x ((1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x )((1 + x )(1 + x )) = 100((1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))
    去掉方程右边的一个括号:
     20(1 + x )(1 + x ) + 20 + 20 ÷ ((1 + x )(1 + x )) × x ((1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x )((1 + x )(1 + x )) = 100(1 + x )(1 + x ) + 100 x ((1 + x )(1 + x ))
     方程两边同时乘以:((1 + x )(1 + x ))
     20(1 + x )(1 + x )((1 + x )(1 + x )) + 20((1 + x )(1 + x )) + 20 x ((1 + x )(1 + x )) + 20 ÷ ((1 + x )(1 + x )(1 + x )) × (1 + x ) = 100(1 + x )(1 + x )((1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x ))
    去掉方程左边的一个括号:
     20 × 1(1 + x )((1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x )) + 20((1 + x )(1 + x )) + 20 x = 100(1 + x )(1 + x )((1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x ))
    去掉方程右边的一个括号:
     20 × 1(1 + x )((1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x )) + 20((1 + x )(1 + x )) + 20 x = 100 × 1(1 + x )((1 + x )(1 + x )) + 100 x (1 + x )((1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x ))
    方程化简为:
     20(1 + x )((1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x )) + 20((1 + x )(1 + x )) + 20 x ((1 + x )(1 + x )) = 100(1 + x )((1 + x )(1 + x )) + 100 x (1 + x )((1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x ))
     方程两边同时乘以:((1 + x )(1 + x )(1 + x ))
     20(1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) = 100(1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x (1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))
    去掉方程左边的一个括号:
     20 × 1((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x )) = 100(1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x (1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))
    去掉方程右边的一个括号:
     20 × 1((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x )) = 100 × 1((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x (1 + x )((1 + x )(1 + x ))
    方程化简为:
     20((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) = 100((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )) + 100 x (1 + x )((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))
     方程两边同时乘以:((1 + x )(1 + x )(1 + x )(1 + x ))
     20((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 20 x (1 + x ) = 100((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 100 x (1 + x )
    去掉方程左边的一个括号:
     20(1 + x )(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 20 x = 100((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 100 x (1 + x )
    去掉方程右边的一个括号:
     20(1 + x )(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 20 x = 100(1 + x )(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )) + 100 x
     方程两边同时乘以:((1 + x )(1 + x )(1 + x )(1 + x )(1 + x ))
     20(1 + x )(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) + 20 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) = 100(1 + x )(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x ))
    去掉方程左边的一个括号:
     20 × 1(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) + 20 x (1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) = 100(1 + x )(1 + x )((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x )) + 100 x ((1 + x )(1 + x ))((1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x ))((1 + x )(1 + x )(1 + x )(1 + x )(1 + x ))


    
        x≈0.308734 ,保留6位小数
    
    有 1个解。


解一元一次方程的详细方法请参阅:《一元一次方程的解法》



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