Question

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

Answer 1

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

Step-by-step explanation:

We have,

$\sqrt{m} +\sqrt{n}-\sqrt{p} = 0$

To find, the value of$(m+n-p)^2$=?

∴ $\sqrt{m} +\sqrt{n}  = \sqrt{p}$

Squaring both sides , we get

$(\sqrt{m} +\sqrt{n})^2=\sqrt{p}^2$

⇒ $(\sqrt{m})^2+(\sqrt{n})^2+2\sqrt{m}\sqrt{n}=p$

⇒ $m+n+2\sqrt{m}\sqrt{n}=p$

⇒ $m+n-p = -2\sqrt{mn}$

Again, squaring both sides , we get

$(m+n-p)^2=(-2\sqrt{mn})^2$

⇒ $(m+n-p)^2=4mn$

Hence, $(m+n-p)^2=4mn$.

Answer 2

Given:

A mathematical relation √m+√n - √p = 0.

To Find:

The value of (m + (n) -  p)².

Solution:

The given problem can be solved using the concepts of algebra.

1. The given relation is √m+√n-√p=0,

2. The given equation can be also written as,

=> √m+√n =√p, ( Consider as equation 1 ).

=> Apply square on both the sides,

=> m + n + 2√(mn) = p,

=> m + n - p = -2√(mn) ( Conisder as equation 2 ).

3. The value of ( m + (n) - p )² can be calculated as,

=> The value of m + (n) - p is equal to -2√(mn), (From Equation 2),

=> ( m + (n) - p )² = (-2√(mn)²  = 4mn.

Therefore, the value of ( m + (n) - p )² is 4mn.