Question : If $x+y+z=0$ and $x^2+y^2+z^2=40$, then what is the value of $x y+y z+z x?$
Option 1: –20
Option 2: 5
Option 3: –5
Option 4: –10
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Answer (1)
22nd Jan, 2024
Correct Answer: –20
Solution :
Given: $x + y + z = 0$ and $x^2+y^2+z^2=40$
⇒ $(x+ y + z)^2= 0$
⇒ $x^2 + y^2 + z^2 + 2(xy + yz + zx) = 0$
⇒ $40 + 2(xy + yz + zx) = 0$
⇒ $2(xy + yz + zx) = - 40$
⇒ $xy + yz + zx = - 20$
Hence, the correct answer is –20.
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