Question

5x

2 + 26y

2 + 10z

2 + 4yz + 14zx + 6xy is a positive semi-definite​

Answer 1

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 2

Answer:

Step-by-step explanation: