Question

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

Answer 1

√m+√n-√p=0
⇒√m+√n=√p
squaring on both sides
⇒m+n+2√(mn)=p
⇒m+n-p=2√(mn)

the value of (m+n-p)²=(-2√(mn))²
                                 =4mn

Answer 2

Given,

√m + √n - √p = 0

To find,

The value of (m+n-p)².

Solution,

The value of (m+n-p)² will be 4mn.

We can easily solve this problem by following the given steps.

According to the question,

√m + √n - √p = 0

√m + √n = √p (Moving √p from the left-hand side to the right-hand side results in the change of the sign from minus to plus.)

Now, square on both sides,

(√m + √n)² = (√p)²

Using the identity (a+b)² = a²+b²+2ab,

(√m)² + (√n)² + 2 √mn = p

m+n+2√mn = p

m+n-p+2√mn = 0

m+n-p = -2√mn

Now, square on both sides,

(m+n-p)² = (-2√mn)²

(m+n-p)² = 4mn

Hence, the value of (m+n-p)² is 4mn.