To solve this equation for 🍌, 🍎, and 🍍, we will first need to use the order of operations to simplify the equation. The order of operations tells us that we should perform any operations inside of parentheses first, so we will start by simplifying each term inside the parentheses on the left-hand side of the equation.
The first term inside the parentheses is 🍎/🍌+🍍, so we will need to divide 🍎 by 🍌 and then add 🍍 to get the simplified form of this term. The second term inside the parentheses is 🍌/🍎+🍍, so we will need to divide 🍌 by 🍎 and then add 🍍 to get the simplified form of this term. The third and final term inside the parentheses is 🍍/🍎+🍌, so we will need to divide 🍍 by 🍎 and then add 🍌 to get the simplified form of this term.
After we have simplified each term inside the parentheses, we can combine all three terms together to get the simplified form of the equation. The result should be something like this:
🍎/🍌 + 🍍 + 🍌/🍎 + 🍍 + 🍍/🍎 + 🍌 = 4
To solve for 🍌, 🍎, and 🍍, we will need to isolate each variable on one side of the equation and then solve for its value. To isolate 🍌, we can move all the terms that contain 🍌 to one side of the equation and all the terms that do not contain 🍌 to the other side. We can do the same thing for 🍎 and 🍍 to solve for their values as well.
Here is an example of how we might isolate 🍌 in the equation above:
To solve for the value of 🍌, we can use the same process, isolating all the terms that contain 🍌 on one side of the equation and all the terms that do not contain 🍌 on the other side. This will give us an equation that we can solve for 🍌. We can then use the value we find for 🍌 to solve for 🍎 and 🍍 using the same process.
To solve for 🍍 in the equation 🍍 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎, we will need to isolate 🍍 on one side of the equation and then solve for its value. To isolate 🍍, we can move all the terms that contain 🍍 to one side of the equation and all the terms that do not contain 🍍 to the other side.
Here is an example of how we might isolate 🍍 in the equation above:
🍍 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎
🍍 + 🍍/🍎 = 4 - 🍎/🍌 - 🍌/🍎
🍍(1 + 1/🍎) = 4 - 🍎/🍌 - 🍌/🍎
🍍 = (4 - 🍎/🍌 - 🍌/🍎) / (1 + 1/🍎)
To solve for the value of 🍍, we can substitute the values of 🍎, 🍌, and 🍎 into this equation and then solve for 🍍. For example, if we set the values of 🍎, 🍌, and 🍎 to 2, 3, and 4, respectively, we would get the following:
In investigating the existence of solutions to (1.1), and more specifically, existence of positive solutions, we discovered that on occasion solutions exist, but the smallest positive solution may be rather large. For example, when N = 896, the smallest positive solution has a, b, c with several trillion digits (we do not list it explicitly)
To solve this equation for 🍌, 🍎, and 🍍, we will first need to use the order of operations to simplify the equation. The order of operations tells us that we should perform any operations inside of parentheses first, so we will start by simplifying each term inside the parentheses on the left-hand side of the equation.
The first term inside the parentheses is 🍎/🍌+🍍, so we will need to divide 🍎 by 🍌 and then add 🍍 to get the simplified form of this term. The second term inside the parentheses is 🍌/🍎+🍍, so we will need to divide 🍌 by 🍎 and then add 🍍 to get the simplified form of this term. The third and final term inside the parentheses is 🍍/🍎+🍌, so we will need to divide 🍍 by 🍎 and then add 🍌 to get the simplified form of this term.
After we have simplified each term inside the parentheses, we can combine all three terms together to get the simplified form of the equation. The result should be something like this:
🍎/🍌 + 🍍 + 🍌/🍎 + 🍍 + 🍍/🍎 + 🍌 = 4
To solve for 🍌, 🍎, and 🍍, we will need to isolate each variable on one side of the equation and then solve for its value. To isolate 🍌, we can move all the terms that contain 🍌 to one side of the equation and all the terms that do not contain 🍌 to the other side. We can do the same thing for 🍎 and 🍍 to solve for their values as well.
Here is an example of how we might isolate 🍌 in the equation above:
🍎/🍌 + 🍍 + 🍌/🍎 + 🍍 + 🍍/🍎 + 🍌 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎
🍍 + 🍍/🍎 + 🍌 - 🍍/🍎 - 🍍/🍎 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎
🍍 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎
To solve for the value of 🍌, we can use the same process, isolating all the terms that contain 🍌 on one side of the equation and all the terms that do not contain 🍌 on the other side. This will give us an equation that we can solve for 🍌. We can then use the value we find for 🍌 to solve for 🍎 and 🍍 using the same process.
To solve for 🍍 in the equation 🍍 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎, we will need to isolate 🍍 on one side of the equation and then solve for its value. To isolate 🍍, we can move all the terms that contain 🍍 to one side of the equation and all the terms that do not contain 🍍 to the other side.
Here is an example of how we might isolate 🍍 in the equation above:
🍍 = 4 - 🍎/🍌 - 🍌/🍎 - 🍍/🍎
🍍 + 🍍/🍎 = 4 - 🍎/🍌 - 🍌/🍎
🍍(1 + 1/🍎) = 4 - 🍎/🍌 - 🍌/🍎
🍍 = (4 - 🍎/🍌 - 🍌/🍎) / (1 + 1/🍎)
To solve for the value of 🍍, we can substitute the values of 🍎, 🍌, and 🍎 into this equation and then solve for 🍍. For example, if we set the values of 🍎, 🍌, and 🍎 to 2, 3, and 4, respectively, we would get the following:
🍍 = (4 - 2/3 - 3/2) / (1 + 1/4)
🍍 = (4 - 0.67 - 1.5) / (1 + 0.25)
🍍 = (2.83) / (1.25)
🍍 = 2.26
🍎 = 3.5
can't tell if this is a bit but if not, the solution is here: https://ami.uni-eszterhazy.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf
holy shit that's nuts!
Before i read it 🍍 = 2.26
integer solutions my friend, though you did find a good way to find non-integer solutions
It's the AI
oh shit that's actually really interesting, thank you for posting
I can't get it to solve for 🍌 and it gave me some very incorrect math earlier.
It's easy if you can use fractions, it's only hard if you're limited to whole numbers