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Attachment 1:
i)
Given that U1 is the solution set.
We observe the equation has no square root signs of any variable and hence chances of getting imaginary roots if coefficients are real is not possible.
Hence If U1 is a subset of R^4, then all coefficients must be real.
i.e. 1-a and b2 must be real. Or a and b must be real.
To be specific if a=1, or b =0 we cannot have solutions for x2 and x4. Hence
The answers are a ≠1 and b≠0
ii)Given that U2 is the set of solutions of the following equation.
To check whether U2 is a subset of R^4.
For U2 to be a subset of R^4, all variables should have real solutions. This is possible only if
For a to be real, discriminant should be positive
i.e.
Hence condition is a should belong to R
To be specific for values of a, we...