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Identity (x+y+z)^2

If x + y + ...

Question

If $(x + y + z) = 9$ and $(x y + y z + z x) = 9$ , then find the value of $(x^{2} + y^{2} + z^{2})$ .

A

49

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B

56

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C

63

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D

81

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Solution

The correct option is B $63$
$[x + y + z]^{2} = x^{2} + y^{2} + z^{2} + 2 [x y + y z + z x] 9^{2} = x^{2} + y^{2} + z^{2} + 2 (9) ∴ x^{2} + y^{2} + z^{2} = 63$

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