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On line Solution of Monovariate Equation：
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
Overview: 7 questions will be solved this time.Among them
☆1 inequalities
☆2 equations
☆1 mathematical statistics
☆1 fraction calculations
☆1 integer calculations
☆1 calculations of prime factor
[ 1/7 Equation]
Work: Find the solution of equation 21x^2-85x+84 = 0 .
Question type: Equation
Solution:
After the equation is converted into a general formula, it is converted into:
( 7x - 12 )( 3x - 7 )=0
From
7x - 12 = 0
3x - 7 = 0
it is concluded that:：
There are 2 solution(s).
解一元二次方程的详细方法请参阅：《一元二次方程的解法》
[ 2/7Inequality]
Assignment:Find the solution set of inequality 21x^2-13x-84 <= 0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
21 * x ^ 2 - 13 * x - 84 <= 0 (1)
From inequality(1)：
-12/7 ≤ x ≤ 7/3
The final solution set is :
-12/7 ≤ x ≤ 7/3
[3/7 Integer column vertical calculation]
Question type: Integer multiplication
Original question: 7536*24987
Solution:
7536*24987 = 188302032
Column vertical calculation:
[ 4/7 Equation]
Work: Find the solution of equation sin2tan2-cos2cot2 = 0 .
Question type: Equation
Solution:
the solutions is:
cot≈2.387200 , keep 6 decimal places
There are 1 solution(s). *Note: Radian.
解方程的详细方法请参阅：《方程的解法》
[ 5/7 Fraction calculation ]
Question type: Fractional subtraction
Original question: 751/2731-5386/9973
Solution:
Divide two fractions with defferent denominators:The denominators of two fractions are 2731 and 9973 respectively,their least common multiple is 27236263
Divide the least common multiple 27236263 by the denominator 2731 of the minuend to get 9973
Multiply the numerator 751 and denominator 2731 of the subtracted number by 9973
Then divide the least common multiple 27236263 by the denominator 9973 of the subtraction to get 2731
Multiply the subtracted numerator 5386 and denominator 9973 by 2731 at the same time
Calculation result:
[6/7 Digtal analysis]
Work：Break 774144 into prime factors.
Question type: Resolving prime factor
Solution:
774144=2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*7
*Note: 774144 has 16 prime factors.
[ 7/7 data statistics ]
Work: Please make statistics on the following data: 1,1,2,3,5,8,13,21,34,55 。
Question type: data statistics
Total data：10
The sum：143
Average value：14.3
Variance：285.01
Standard deviation：16.88224
*Note: Totally 5 items are counted.
>>注：本次最多计算 7 道题。
☆1 inequalities
☆2 equations
☆1 mathematical statistics
☆1 fraction calculations
☆1 integer calculations
☆1 calculations of prime factor
[ 1/7 Equation]
Work: Find the solution of equation 21x^2-85x+84 = 0 .
Question type: Equation
Solution:
After the equation is converted into a general formula, it is converted into:
( 7x - 12 )( 3x - 7 )=0
From
7x - 12 = 0
3x - 7 = 0
it is concluded that:：
| x1= | 12 7 |
| x2= | 7 3 |
There are 2 solution(s).
解一元二次方程的详细方法请参阅：《一元二次方程的解法》
[ 2/7Inequality]
Assignment:Find the solution set of inequality 21x^2-13x-84 <= 0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
21 * x ^ 2 - 13 * x - 84 <= 0 (1)
From inequality(1)：
-12/7 ≤ x ≤ 7/3
The final solution set is :
-12/7 ≤ x ≤ 7/3
[3/7 Integer column vertical calculation]
Question type: Integer multiplication
Original question: 7536*24987
Solution:
7536*24987 = 188302032
Column vertical calculation:
| 7 | 5 | 3 | 6 | ||||||||||
| ✖ | 2 | 4 | 9 | 8 | 7 | ||||||||
| 5 | 2 | 7 | 5 | 2 | |||||||||
| 6 | 0 | 2 | 8 | 8 | |||||||||
| 6 | 7 | 8 | 2 | 4 | |||||||||
| 3 | 0 | 1 | 4 | 4 | |||||||||
| 1 | 5 | 0 | 7 | 2 | |||||||||
| 1 | 8 | 8 | 3 | 0 | 2 | 0 | 3 | 2 | |||||
[ 4/7 Equation]
Work: Find the solution of equation sin2tan2-cos2cot2 = 0 .
Question type: Equation
Solution:
the solutions is:
cot≈2.387200 , keep 6 decimal places
There are 1 solution(s). *Note: Radian.
解方程的详细方法请参阅：《方程的解法》
[ 5/7 Fraction calculation ]
Question type: Fractional subtraction
Original question: 751/2731-5386/9973
Solution:
751 2731 | － | 5386 9973 |
Divide the least common multiple 27236263 by the denominator 2731 of the minuend to get 9973
Multiply the numerator 751 and denominator 2731 of the subtracted number by 9973
Then divide the least common multiple 27236263 by the denominator 9973 of the subtraction to get 2731
Multiply the subtracted numerator 5386 and denominator 9973 by 2731 at the same time
| = | 7489723 27236263 | － | 14709166 27236263 |
| = | - | 7219443 27236263 |
[6/7 Digtal analysis]
Work：Break 774144 into prime factors.
Question type: Resolving prime factor
Solution:
774144=2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*7
*Note: 774144 has 16 prime factors.
[ 7/7 data statistics ]
Work: Please make statistics on the following data: 1,1,2,3,5,8,13,21,34,55 。
Question type: data statistics
Total data：10
The sum：143
Average value：14.3
Variance：285.01
Standard deviation：16.88224
*Note: Totally 5 items are counted.
>>注：本次最多计算 7 道题。