- #1
nek9876
- 3
- 0
I'm trying to help my son with homework and can't get the following problem
\(\displaystyle x\sqrt{3}+x\sqrt{2}=1\)
Please help
\(\displaystyle x\sqrt{3}+x\sqrt{2}=1\)
Please help
Last edited by a moderator:
Start by factoring the x from the left hand side:nek9876 said:I'm trying to help my son with homework and can't get the following problem
\(\displaystyle x\sqrt{3}+x\sqrt{2}=1\)
Please help
nek9876 said:I'm trying to help my son with homework and can't get the following problem
\(\displaystyle x\sqrt{3}+x\sqrt{2}=1\)
Please help
nek9876 said:Thanks for the help.
Ok so we had thought about factoring out the X and then we thought the next step would be to square both sides.
If we do that the one side is obviously 1, but then does the other side become 5xe^{2}?
nek9876 said:That makes sense and I see the error we made in squaring it out.
So based on dividing both sides we would then isolate the x and have
\(\displaystyle x=\frac{1}{\sqrt{2}+\sqrt{3}}\)
So then we do have x isolated, I would think at this point that this is the final answer
nek9876 said:Also one question when typing this in, I must be using the wrong symbols on the side to hit square root, how do
I put it in the correct form so it looks better in the future?
Again thanks for the help
A radical equation is an equation that contains a radical, which is a mathematical symbol used to indicate the root of a number. The most common radicals are the square root (√) and the cube root (3√). Solving radical equations involves finding the value of the variable that makes the equation true.
The general process for solving radical equations involves isolating the radical on one side of the equation and then raising both sides to the appropriate power to eliminate the radical. This process is repeated until the variable is isolated and its value can be determined.
Extraneous solutions are solutions that do not satisfy the original equation, even though they may satisfy the simplified equation. This can occur when raising both sides of the equation to a power, as it can introduce solutions that were not present in the original equation. Checking for extraneous solutions ensures that the final solution is valid.
One common mistake is forgetting to check for extraneous solutions. Another mistake is incorrectly simplifying the radical, which can lead to incorrect solutions. It is also important to be careful when raising both sides of the equation to a power, as this can introduce extraneous solutions.
You can check your solution by plugging it back into the original equation and simplifying. If the resulting equation is true, then the solution is correct. It is also a good idea to double-check for any extraneous solutions.