Is there a real solution to: B &#x2264;<!-- ≤ --> A , B &#x2264;<!-- ≤ --> C

Gauge Terrell 2022-07-07 Answered
Is there a real solution to: B A , B C? Namely, is there s = ( α , β , γ , δ ) R 4 such that B ( s ) A ( s ) , B ( s ) C ( s )?
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Answers (1)

Sanaa Hinton
Answered 2022-07-08 Author has 15 answers
Let A ~ ( s ) = A ( s ) B ( s ) and C ~ ( s ) = C ( s ) B ( s )
Since A , B , C are homogeneous of degree 3, so do A ~ and C ~ . For any s R 4 , we have A ~ ( s ) = A ~ ( s ) and C ~ ( s ) = C ~ ( s ).
Using continuity of A ~ , we can find a point t R 4 with | t | = 1 and A ~ ( t ) = A ~ ( t ) = 0. Since at least one of C ~ ( t ) or C ~ ( t ) 0. We have find a s = t or t such that | s | = 1 and
A ~ ( s ) = 0 , C ~ ( s ) 0 A ( s ) = B ( s ) , C ( s ) B ( s )

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