If $\sqrt{x} -\sqrt{y}+\sqrt{z}=0$ , which of the following is true?

Correct answer marked below

x^2+y^2+z^2=xy+xz+yz

x^2+y^2+z^2=2xy+2xz+2yz

Correct

x^2+y^2-z^2=2xy+2xz-2yz

x^2-y^2-z^2=xy+xz+yz

x^4+y^4+z^4=2xy+2xz+2yz

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Explanation

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Official Explanation

Official

In case one does not remember the formula, plugging smart numbers will be highly effective.

Let

x=z=1

and

y=4

. This satisfies our stem equation.

Test the values in the options and the option where

LHS=RHS

will be correct.…

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What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.