Consider the equation 
.
First, you can use the substitution 
, then 
and equation becomes 
. This equation is quadratic, so
.
Then you can factor this equation:
.
Use the made substitution again:
.
You have in each brackets the expression like 
that is equal to 
. Thus,
![x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)](https://tex.z-dn.net/?f=%20x%5E3%2B5%3D%28x%2B%5Csqrt%5B3%5D%7B5%7D%29%28x%5E2-%5Csqrt%5B3%5D%7B5%7Dx%2B%5Csqrt%5B3%5D%7B25%7D%29%20%2C%5C%5Cx%5E3%2B1%3D%28x%2B1%29%28x%5E2-x%2B1%29%20%20%20)
and the equation is
![(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0](https://tex.z-dn.net/?f=%20%28x%2B%5Csqrt%5B3%5D%7B5%7D%29%28x%5E2-%5Csqrt%5B3%5D%7B5%7Dx%2B%5Csqrt%5B3%5D%7B25%7D%29%28x%2B1%29%28x%5E2-x%2B1%29%3D0%20%20%20)
.
Here ![x_1=-\sqrt[3]{5} , x_2=-1](https://tex.z-dn.net/?f=%20x_1%3D-%5Csqrt%5B3%5D%7B5%7D%20%2C%20x_2%3D-1%20)
and you can sheck whether quadratic trinomials have real roots:
1. ![D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}](https://tex.z-dn.net/?f=%20D_1%3D%28-%5Csqrt%5B3%5D%7B5%7D%29%20%5E2-4%5Ccdot%20%5Csqrt%5B3%5D%7B25%7D%3D%5Csqrt%5B3%5D%7B25%7D%20-4%5Csqrt%5B3%5D%7B25%7D%20%3D-3%5Csqrt%5B3%5D%7B25%7D%20%20%3C0%20)
.
2. 
.
This means that quadratic trinomials don't have real roots.
Answer:
If you need complex roots, then
![x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}](https://tex.z-dn.net/?f=%20x_%7B3%2C4%7D%3D%5Cdfrac%7B%5Csqrt%5B3%5D%7B5%7D%5Cpm%20i%5Csqrt%7B3%5Csqrt%5B3%5D%7B25%7D%7D%7D%7B2%7D%20%20%20%2C%5C%5C%20%5C%5Cx_%7B5%2C6%7D%3D%5Cdfrac%7B1%5Cpm%20i%5Csqrt%7B3%7D%7D%7B2%7D%20%20%20%20)
.
Answer:
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Answer:
-4
Step-by-step explanation:
Use the given value of f(1) to find f(2):
f(2) = f(1) · (-1/2) = (-16)(-1/2) = 8
Now, we can find f(3) using f(2):
f(3) = f(2) · (-1/2) = (8)(-1/2)
f(3) = -4
Divide 30 by 3 and you get 10. Divide 30 by 2 and your get 15. Add 15 to 10 and you get 25. 25 is your answer.
A simple way you could solve this is by drawing a tape graph.
Draw a long rectangular box.
Cut the box into 8 pieces, seeing as how 5/8 of the coins are dimes.
We have to take 48 and divide it by 8, we get 6, so now we know how many dimes are evenly split into each piece.
Now color in 5 pieces of the tape.
This represents the 5 in 5/8.
Now to find the number of coins, simply multiply 5 by 6, you get the answer of 30.
I hope this helps, if you are confused with any part of my explanation, ask and I will clarify.
