Question

A^2 + 4b = c^2. If b is known is there a way to find a ?

Answer 1

Given,
`a^2 + 4b = c^2`
The relation will be
`c^2-a^2=4b`
`=>a^2=4b-c^2`
`=>sqrt(a^2)=sqrt(c^2-4b)`
`=>a=sqrt(c^2-4b)`

Explanation:

Since you haven't mentioned the value of `"b"` in the question, I can only show the relation between `"a"` and `"b"`.
We know that `a^2 + 4b = c^2`
We will group the like terms i.e. `a^2` and `b^2` on one side and take `4"b"` on the other side.
`a^2-c^2=4b`
Since `a^2-c^2` is equal to `4"b"`, (`a^2-c^2`)must be a multiple of 4. We can try to assume the values as different perfect squares whose difference is a multiple of 4.
For example `3^2-1^2=9-1=8` (which is a multiple of 4)

Answer 2

Given, `a^2 + 4b = c^2` which can be solved for a yielding `a=sqrt(c^2-4b)`

So if `c and b` are known, you can find `a`.

Explanation:

`a^2 + 4b = c^2`

Isolate `a^2`.

`a^2 = c^2 - 4b`

Take square root of both sides:

`a=sqrt(c^2-4b)`

So, you can not find `a` knowing just `b`, you would also need to know `c`.

I hope this helps,
Steve