If x + y + z = 13 and x2 + y2 + z2 = 69, then xy + z (x

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x + y + z = 13
x² + y² + z² = 69
(x + y + z)²
= x² + y² + z² +2 (xy + yz + zx)
⇒ (13)² = 69 + 2 (xy + yz + zx)
⇒ 2 (xy + yz + zx)
= 169 – 69 = 100

⇒ xy + yz + zx =	100	= 50
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