Write as a Vector Equality p^2+4h^2=4 , h=p+1

Problem

p2+4*h2=4,h=p+1

Solution

1. Identify the variables and the structure of the equations. We have a system consisting of a quadratic equation and a linear equation involving variables p and h

2. Represent the variables as a vector v Let v=[[p],[h]]

3. Rewrite the linear equation h=p+1 in the standard form −p+h=1

4. Express the system using vector and matrix notation. The quadratic part can be written as a quadratic form vT*A*v=4 where A=[[1,0],[0,4]]

5. Combine the information into a single vector statement. The relationship between p and h can be expressed as the vector [[p],[h]] satisfying both the scalar product and the linear constraint.

Final Answer

[[p,h]]*[[1,0],[0,4]]*[[p],[h]]=4,[[−1,1]]*[[p],[h]]=1

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