5x
2 + 26y
2 + 10z
2 + 4yz + 14zx + 6xy is a positive semi-definite
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Yes, 5x²+26y²+10z²+4yz+4zx+6xy is semi-definite.
Given:
5x²+26y²+10z²+4yz+4zx+6xy
To find: whether 5x²+26y²+10z²+4yz+4zx+6xy is semi-definite or not?
Solution:
4yz= should be interpreted as 2. a.b,
(2y+z)²=2y²+z²+4yz
putting value,
5x²+24y²+9z²+4zx+6xy+(2y+z)²
6xy interpretation,
(3y+x)²=9y²+x²+6xy
4x²+15y²+9z²+4zx+(2y+z)²+(3y+x)²
4zx interpretation,
(2x+z) ²=4x²+z²+4xz
15y²+8z²+(2x+z)²+(2y+ z)²+(3y+x)²
As, all the variables are positive so it is positive semi-definite.
Yes, 5x²+26y²+10z²+4yz+4zx+6xy is semi-definite.
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Answer:
Step-by-step explanation:
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