Question
Download Solution PDFIf x + y + z = 0 and x2 + y2 + z2 = 40, then what is the value of xy + yz + zx?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x + y + z = 0
x2 + y2 + z2 = 40
Concept used:
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
Calculation:
x + y + z = 0
⇒ (x + y + z)2 = 02
⇒ x2 + y2 + z2 + 2(xy + yz + zx) = 0
⇒ 40 + 2(xy + yz + zx) = 0
⇒ 2(xy + yz + zx) = - 40
⇒ xy + yz + zx = - 20
∴ The required answer is - 20.
Last updated on Jul 8, 2025
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