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The solution of a simple algebraic problem
2022-07-07 05:57:00 【Zhuoqing】
§01 generation Numerical solution
Yes An interesting topic , The difference between skill calculation and numerical calculation is shown .
Known variables a,b The difference between square and a,b The product of the , seek a+b Value . The direct impulse of people who have studied mathematics , It is based on ab=3, obtain b=3/a. To the first expression You can list about a The equation of . Solving this equation . You can get a The value of square according to a Square is greater than 0, You can get a Unique value of , The value of abandonment is more complex . But this is the result a The value of .
Next, according to b=3/a, You can know b The value of , Finally get a+b The value of . Simplifying this expression is a nightmare . Here are a,b,a+b Numerical solution of .
This solution process is a standard algebraic solution , But the final result of simplification is not very friendly . Is there any other good method besides direct solution ?
Here is another solution . For the sake of a+b Value , Let's see if we can get (a+b) The square of ? an a+b The square of , You can see that there are three items , In the middle of the ab The product is known , but a square +b Square requires .
For the sake of a The square of +b The square of , What will be known (a Square minus b square ) Continuous square , You can get a The fourth power of , subtract 2 Times a Fang b Fang , add b The fourth power of . According to known conditions , It's equal to 9 The square of . Add the equation left and right at the same time 4bz Of a Fang b Fang , Left got a Canada b Square term of square . The right side can be calculated to be equal to 117.
And that gives us a Canada b The value of the square , Through both sides at the same time square , You can get a Canada b The value of the square . Will find a Canada b Square into the initial expression , You can get a Add b The value of square . Square off both sides , You can get a+b The value of .
Compare the two methods to solve , You can see that their results are the same . The first method , Start simple , The later simplification is complex . The second method , Need to use math tricks , But the result is easier to simplify . Do you think the internal method is better ?
※ total junction ※
Ben This paper tests the use of PAD Complete the process of solving algebraic equations .
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