If x + 4y + 92? + byz - 3zx - 2xy = 0, then equal all of them
Answers
Answered by
0
Step-by-step explanation:
f(x,y,z)=x
2
+4y
2
+9z
2
−6yz−3zx−2xy
=
2
1
[2x
2
+8y
2
+18z
2
−12yz−6zx−4xy]
=
2
1
[(x
2
−4xy+4y
2
)+(x
2
−6zx+9z
2
)+(9z
2
−12yz+4y
2
)]
=
2
1
[(x−2y)
2
+(x−3z)
2
+(3z−2y)
2
]
Hence
f(x,y,z)=
2
1
[(x−2y)
2
+(x−3z)
2
+(3z−2y)
2
]
Since x,y,xϵR hence f(x,y,z)≥0.
Hope it would be helpful to you
Similar questions