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Algebraic Identity (a-b)^3

If x + y + ...

Question

If $x + y + z = 6, x y + y z + z x = 11$ . Find the value of $x^{2} + y^{2} + z^{2} .$

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Solution

$x + y + z = 6$

Squaring on both sides, we get

$x^{2} + y^{2} + c^{2} + 2 (x y + y z + z x) = 6^{2}$

$x^{2} + y^{2} + c^{2} + 2 (11) = 36$

$x^{2} + y^{2} + c^{2} = 36 - 22$

$x^{2} + y^{2} + c^{2} = 14$

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Similar questions

x - y + z = 5

x^{2} + y^{2} + z^{2} = 49

, find the value of :

z x - x y - y z

x + y + z = 10

x^{2} + y^{2} + z^{2} = 40

x y + y z + z x

x^{2} + y^{2} + z^{2} - x y - y z - z x = 0

then the value of

\frac{x + y}{z}

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what will be the value of

\frac{x^{2} + y^{2} + z^{2}}{- (x y + y z + z x)} ?

x = 2, y = - 1, z = 4

; find the value of the following expression

x^{2} + y^{2} + z^{2} - x y - y z - z x

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