Question
Download Solution PDFIf (x + y + z) = 23 and x2 + y2 + z2 = 179, then find the value of (xy + yz + zx).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
If (x + y + z) = 23 and x2 + y2 + z2 = 179, then find the value of (xy + yz + zx).
Formula used:
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
Calculation:
(x + y + z)2 = 232 = 529
x2 + y2 + z2 = 179
So, 529 = 179 + 2(xy + yz + zx)
⇒ 529 - 179 = 2(xy + yz + zx)
⇒ 350 = 2(xy + yz + zx)
⇒ 350/2 = xy + yz + zx
⇒ xy + yz + zx = 175
∴ The correct answer is option (3).
Last updated on Jul 15, 2025
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