Question

The square root of x² + y2 + z2 -
2xy + 2yz - 2zx


​

Answer 1

Answer:

(--x +y+z)

..................

Answer 2

Answer:

√{x² + y² + z² - 2xy + 2yz - 2zx} = (x - y - z)

.

.

or

√{x² + y² + z² - 2xy + 2yz - 2zx} = (-x+y+z)

is also correct answer.

Explanation:

as we know that:-

(x + y)² = x² + 2xy +y²

.

.

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

.

.

simillarly

.

.

(x - y - z)² = x² + y² + z² - 2xy + 2yz - 2zx

.

Or

.

x² + y² + z² - 2xy + 2yz - 2zx = (x - y - z)²

now taking √ both side...

√{x² + y² + z² - 2xy + 2yz - 2zx} = √{(x - y - z)²}

.

.

√{x² + y² + z² - 2xy + 2yz - 2zx} = (x - y - z)