Question

If x + y + z=10 and xy + yz + zx= 40,evaluate x² + y² + z².

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Answer 1

$(x + y + z)^{2} = (10)^{2} \\ squaring \: both \: sides \\ x^{2} + y^{2} + z ^{2} + 2(xy + yz + xz) = 100 \\ x^{2} + y^{2} + z ^{2} = 100 - 2(xy + yz + xz) \\ x^{2} + y^{2} + z ^{2} = 100 - 2(40) \\ x^{2} + y^{2} + z ^{2} = 100 - 80 \\ x^{2} + y^{2} + z ^{2} = 20$
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Answer 2

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