So the first step is to simply set up the problem based on what we are given. So here have two numbers, we are going to call the first number x and the second one y. With that now addressed, we can now proceed with the setup.
So the difference between the squares of the numbers is 24. So we have:
Then it says that three times the square of the first number (which we said was x) increased by the square of the second number is 76. So:
Now we can see that this is simply a system of equations and we can use elimination to solve this! We even have the setup already as the coefficients in front of our y are opposite in sign and are equal. So:
We can cancel our y squared terms out and that leaves, when we add the equations together:
We can then solve for x by diving by four and taking the square root of the result.
Therefore, x = ±5
We have both negative and positive answers because if we squared -5 or +5 they would both give us 25. So we cant rule a negative answer out yet.
So now we can plug in x = -5 or +5 to either equation to solve for y as so:
So y = ±1
In this case both negative and positive versions of our answer work (you can also double check), so we are left with:
I had a test like this so I kinda know wut the answer is a few weeks or so ago but u need to multiply -5 • 5 (which would be negative since it has one negative sign) then multiply -5 • -5 (since it has another negative it’s positive) then u just multiply the answers that u got from the times 5 u did -bonus if it’s 1 negatives it’s a negative but if it’s 2 negatives it’s a positive
On a phone here and no access to paper but you must first find the midpoint of AC which is the average of the coordinates. The perpendicular bisector will have a gradient that multiplies by AC's gradient to make -1. This will obviously pass through its mid point so as long as you know how to use y=mx+c you should be good.