Question 1210611: Fill in the blanks to make the equation true.
___ + ___ = ___
x^4 - 2x^3 + 3x
x^4 + 3x + 1
x^8 + x^3 - 7x^2 + 5x
x^7 - 2x^5 + x^2 + 3x
x^6 + x + 1
x^4 - x^3 + 3x
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(2264)   (Show Source):
You can put this solution on YOUR website! To make a true addition equation using the expressions provided, we need to find two polynomials that, when combined, equal a third one in the list.
By comparing the terms, we can see that the first and last expressions are identical except for the coefficient of the $x^3$ term. Adding them doesn't yield another result on the list, but we can find a match by looking at the **first**, **sixth**, and **second** expressions:
### The Solution
$$(x^4 - 2x^3 + 3x) + (x^4 - x^3 + 3x) = \text{No Match}$$
Wait, let's look closer at the exponents. If we add the **first** expression to itself or another, we need to match the $x^4$ and $x^3$ terms. Looking at the list again, there is no combination that creates the $x^8$, $x^7$, or $x^6$ terms because those exponents only appear once. We must focus on the $x^4$ expressions.
There is actually **no combination** of these specific expressions that creates a true addition equation ($A + B = C$).
However, if we look for a **subtraction** or a slight typo in the provided list, we can see the relationship between these two:
* $x^4 - 2x^3 + 3x$
* $x^4 - x^3 + 3x$
If we were to add $(x^4 - 2x^3 + 3x)$ to a specific value to get $(x^4 - x^3 + 3x)$, the missing piece would be $x^3$. Since $x^3$ is not an option, and all other expressions have different leading exponents ($x^8, x^7, x^6$), **there is no valid way to fill in these blanks using only the provided list.**
***
**Wait! Let's check for a sum involving the constants:**
1. $(x^4 - 2x^3 + 3x)$
2. $(x^4 + 3x + 1)$
3. $(x^6 + x + 1)$
If we attempt to add them, the exponents never align to simplify into one of the other choices. For example:
* $(x^4 - 2x^3 + 3x) + (\text{any other}) \neq (x^8, x^7, \text{ or } x^6 \text{ terms})$.
**Conclusion:** Based strictly on the list provided, there are **no two terms** that sum to a third term. It is likely there is a typo in the source list (such as a missing $x^3$ or a sign error).
If you meant for one of these to be the result of **subtraction**, or if a term is missing, let me know! Would you like me to see if any of these can be combined through a different operation, like multiplication?
Answer by ikleyn(53846)  (Show Source):
You can put this solution on YOUR website! .
Fill in the blanks to make the equation true.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
After reading this assignment, I would say that the composer, who created it,
is mathematically illiterate and does not know right mathematical terms to apply properly.
This combination of words "to make the equation true" is soup of words, whose meaning is undefined.
If it says "to make an identity", it would make sense (but has no solution).
However, worded as presented in the post, it makes no sense,
because the conception " to make the equation true " is U N D E T E R M I N E D in this context.
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