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1. x + y + z = 15 এবং x2 + y2 + z2 = 83 হলে, xy + yz + zx এর মান কোনটি?
- A. 71
- B. 71
- C. 71
- D. 71
Answer: Option A
Explanation:
দেওয়া আছে,
x^2+y^2+z^2=5,x+y+z=3,
yz+zx−xy
(x+y+z)2=(x2+y2+z2)+ 2(xy-yz-zx)
⇒(15)2=83+2(xy-yz-zx)
⇒225=83 +2 (xy-yz-zx)
⇒2(xy-yz-zx)=-142
⇒xy-yz-xy=-71
⇒yz +zx+xy=71
x^2+y^2+z^2=5,x+y+z=3,
yz+zx−xy
(x+y+z)2=(x2+y2+z2)+ 2(xy-yz-zx)
⇒(15)2=83+2(xy-yz-zx)
⇒225=83 +2 (xy-yz-zx)
⇒2(xy-yz-zx)=-142
⇒xy-yz-xy=-71
⇒yz +zx+xy=71
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