হলে এর মান -
Created: 3 weeks ago |
Updated: 1 week ago
best des
(x+2y)2+(y+2z)2+(z+2x)2
=x2+4xy+4y2+y2+4yz+4z2+z2+4zx+4x2
=x2+y2+z2+4xy+4yz+4zx+4x2+4y2+4z2
=2+4*1+4*2
=14
(X+2y)2+(y+2z)2 +(z+2x)2
=x2 +4xy+4y2 +y2 +4yz+4z2 +z2 +4xz+4x2
=x2 +y2 +z2 +4x2 +4y2 +4z2 +4xy+4yz+4xz
=( x2 +y2 +z2 ) +4( x2 +y2 +z2 ) +4(xy+yz+xz)
=2+4.2+4.1
=2+8+4
=14
Ans:14
এখানে,
x^2+y^2+z^2 = 2
xy+yz+zx = 1
প্রদত্ত রাশি = (x+2y)^2 + (y+2z)^2 + (z+2x)^2
= x^2 + 4xy + 4y^2 + y^2 + 4yz + 4z^2 + z^2 +
4zx + 4x^2
= 5x^2 + 5y^2 + 5z^2 + 4xy + 4yz + 4zx
= 5(x^2+y^2+z^2) + 4(xy+yz+zx)
= 5×2 + 4×1
= 10 + 4
= 14
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