Question

If root a+root b- root c =0 find the value of (a+b-c) ^2

Answer 1

√ (a+b-c) = 0 (given)

=>(a+b-c) = 0 (squaring on both sides)

=>(a+b-c)^2 =0 (again squaring on both sides)

Hence, the answer is 0.

Answer 2

The value of (a+b-c)² is 4ab.

Given:

root a+root b- root c =0

To Find:

The value of (a+b-c) ^2.

Solution:

We are required to find the value of (a+b-c) ^2.

We are given that

√a+√b-√c = 0

The above equation can be written in power form as,

a^(1/2)+b^(1/2) = c^(1/2)

On taking squares on both sides we get

(a^(1/2)+b^(1/2))² = (c^(1/2))²    ---------(1)

By using (a+b)² = a²+2ab+b² in above equation(1)

a + 2√ab + b = c

a+b-c = -2√ab, we get

On taking square on both sides we get

(a+b-c)² = (-2√ab)²

(a+b-c)² = 4ab

Therefore, The value of (a+b-c)² is 4ab.

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