जर x + y + z = 0 आणि x2 + y2 + z2 = 40 असेल, तर xy + yz + zx चे मूल्य किती?

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4)
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  1. -20
  2. 5
  3. -5
  4. -10

Answer (Detailed Solution Below)

Option 1 : -20
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Detailed Solution

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दिलेल्याप्रमाणे:

x + y + z = 0

x2 + y2 + z2 = 40

वापरलेली संकल्पना:

(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)

गणना:

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

∴ आवश्यक उत्तर -20 आहे.

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