Question

If root m + root n - root p=0
Find (m+n-p)^2

Answer 1

I hope this answer is correct

Answer 2

Answer:

Heya........ ❤️

Here is ur answer :

If √m + √n + √p = 0, what is the value of (m+n-p) ^2?

There are two ways to look at it, algebraically or by number theory.

Firstly, √m + √n = - √p .

On squaring, m + n + √2mn = p.

Rearranging, m + n - p = - √2mn.

Which again on squaring gives, (m + n - p)^2 = 2mn

But by definition of square root we always take the non negative value of the function. This contradicts the statement √m + √n = - √p , fro positive values of m, n and p.

Hence the only valid solution is m = n = p = 0, giving (m + n - p)^2 = 0.

Here algebra gives us an answer in terms of variables without caring if the function is implicit or explicit, as y = √x and y ^2 = x have different solutions, Hence it is necessary to always check the validity of solutions by basics of number theory.

√m + √n - √p = 0

√m+ √n = √p

Squaring on both sides,

(√m + √n)^2 = (√p)^2

m + n + 2√mn = p

m + n - p = -2√mn

Therefore,

(m + n -p)^2 = (-2√mn)^2

(m + n -p)^2 = 4mn

Hope it will help you ✌