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Expansion of (x^2 - y^2)

If x+y+z=10 a...

Question

If $x + y + z = 10$ and $x y + y z + z x = 20$ , what is the value of $x^{2} + y^{2} + z^{2}$ ?

A

40

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B

60

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C

80

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D

50

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Solution

The correct option is B 60
We know,

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

Given,
x + y + z = 10 and xy + yz + zx = 20

$∴$
$(10)^{2}$ = $x^{2} + y^{2} + z^{2}$ + 2(20)
$\Rightarrow$ $100 - 40$ = $x^{2} + y^{2} + z^{2}$
$\Rightarrow$ $x^{2} + y^{2} + z^{2}$ = $60$

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Similar questions

x + y + z = 10

x y + y z + z x = 20

, what is the value of

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

x + y - z = 4

x^{2} + y^{2} + z^{2} = 50

, find the value of

x y - y z - z x

x - y + z = 5

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

, then the value of

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x + y + z = 0,

what will be the value of

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

x + y + z = 10

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

x y + y z + z x

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