数学
         
语言:中文    Language:English
在线解一元方程:
    直接输入任意的一元方程,然后点击“下一步”按钮,即可获得方程的解。
    它支持包含数学函数的方程。
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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 952 = 100÷(1+r)+100÷((1+r)×(1+r))+1100÷((1+r)×(1+r)×(1+r)) 的解.
    题型:方程
    解:原方程:
     952 = 100 ÷ (1 + r ) + 100 ÷ ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r ))
     方程两边同时乘以:(1 + r )
     952(1 + r ) = 100 + 100 ÷ ((1 + r )(1 + r )) × (1 + r ) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    去掉方程左边的一个括号:
     952 × 1 + 952 r = 100 + 100 ÷ ((1 + r )(1 + r )) × (1 + r ) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    去掉方程右边的一个括号:
     952 × 1 + 952 r = 100 + 100 ÷ ((1 + r )(1 + r )) × 1 + 100 ÷ ((1 + r )(1 + r )) × r + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    方程化简为:
     952 + 952 r = 100 + 100 ÷ ((1 + r )(1 + r )) + 100 ÷ ((1 + r )(1 + r )) × r + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
     方程两边同时乘以:((1 + r )(1 + r ))
     952((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )) = 100((1 + r )(1 + r )) + 100 + 100 ÷ ((1 + r )(1 + r )) × r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )((1 + r )(1 + r ))
    去掉方程左边的一个括号:
     952(1 + r )(1 + r ) + 952 r ((1 + r )(1 + r )) = 100((1 + r )(1 + r )) + 100 + 100 ÷ ((1 + r )(1 + r )) × r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )((1 + r )(1 + r ))
    去掉方程右边的一个括号:
     952(1 + r )(1 + r ) + 952 r ((1 + r )(1 + r )) = 100(1 + r )(1 + r ) + 100 + 100 ÷ ((1 + r )(1 + r )) × r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )((1 + r )(1 + r ))
     方程两边同时乘以:((1 + r )(1 + r ))
     952(1 + r )(1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    去掉方程左边的一个括号:
     952 × 1(1 + r )((1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    去掉方程右边的一个括号:
     952 × 1(1 + r )((1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100 × 1(1 + r )((1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r
    方程化简为:
     952(1 + r )((1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100(1 + r )((1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))
     方程两边同时乘以:((1 + r )(1 + r )(1 + r ))
     952(1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )) = 100(1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    去掉方程左边的一个括号:
     952 × 1((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100(1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    去掉方程右边的一个括号:
     952 × 1((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100 × 1((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))
    方程化简为:
     952((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) = 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    去掉方程左边的一个括号:
     952(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    去掉方程右边的一个括号:
     952(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))
    去掉方程左边的一个括号:
     952 × 1(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))
    去掉方程右边的一个括号:
     952 × 1(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) = 100 × 1(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    方程化简为:
     952(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 = 100(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100
    去掉方程左边的一个括号:
     952 × 1((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r = 100(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100
    去掉方程右边的一个括号:
     952 × 1((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r = 100 × 1((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r


    
        r≈0.119984 ,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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