Question

find the square root of x square + Y square + Z square - 2 x y - 2 y z + 2 z x​

Answer 1

$\sqrt{x^2+y^2+z^2-2xy-2yz+2zx}$ = x - y + z

Step-by-step explanation:

We have,

$\sqrt{x^2+y^2+z^2-2xy-2yz+2zx}$

To find, $\sqrt{x^2+y^2+z^2-2xy-2yz+2zx}$ = ?

∴ $\sqrt{x^2+y^2+z^2-2xy-2yz+2zx}$

= $\sqrt{x^2+(-y)^2+z^2+2x(-y)+2(-y)z+2zx}$

Using the algebraic identity,

$(a+b+c)^{2} =a^2+b^2+c^2+2ab+2bc+2ca}$

Put b = - b, we get

$(a-b+c)^{2} =a^2+(-b)^2+c^2+2a(-b)+2(-b)c+2ca}$

= $\sqrt{(x-y+z)^{2} }$

= x - y + z

∴ $\sqrt{x^2+y^2+z^2-2xy-2yz+2zx}$ = x - y + z

Answer 2

Step-by-step explanation:

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