Question:
Solution:
Let the following equation:
![\sqrt[]{12-x}=\text{ x}](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B12-x%7D%3D%5Ctext%7B%20x%7D)
this is equivalent to:
![(\sqrt[]{12-x})^2=x^2](https://tex.z-dn.net/?f=%28%5Csqrt%5B%5D%7B12-x%7D%29%5E2%3Dx%5E2)
this is equivalent to:

this is equivalent to:

thus, we can conclude that
x= 3.
Answer:

Step-by-step explanation:
a trinomial that cannot be factored has no real roots.
here is one:

After graphing this trinomial has no intersections points with the x-axis wich means it has no roots
Answer:
Numbers are 32, and 26.
Step-by-step explanation:
58 / 2 = 29
29 + 3 = 32 (large number)
29 - 3 = 26 (small number)
Answer:
The smallest value of p+q is 11
It happens when p = 6 and q = 5.
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Explanation:
Let's factor 180 in such a way that exactly one factor is a perfect square.
I'll ignore the trivial factor of 1.
Here are the possible factorizations we could go with:
180 = 4*45
180 = 9*20
180 = 36*5
Those factorizations then lead to the following

Then we have
p+q = 2+45 = 47
p+q = 3+20 = 23
p+q = 6+5 = 11
The smallest value of p+q is 11 and it happens when p = 6 and q = 5.
Side note: p+q is smallest when we go with the largest perfect square factor.
As it is proved that the equation has no solution, Derick is correct
Step-by-step explanation:
Given

We have to solve the equation in order to check if Derick was solved the equation correctly or not.
So,
Applying distributive property first

As the variable is already cancelled in the equation there is no unique solution.
In order for an equation to have infinite solutions the constant on both sides of equation should be same which is not the case in the given equation
So,
As it is proved that the equation has no solution, Derick is correct
Keywords: Linear equations, variables
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