Find the Domain 5a^2+3b^2+3d^2+2ab+2ad+6bd=7g^2+4h^2

Problem

5*a^2+3*b^2+3*d^2+2*a*b+2*a*d+6*b*d=7*g^2+4*h^2

Solution

1. Identify the type of equation. This is a multivariable equation involving five variables: a b d g and h

2. Analyze the expression for restrictions. The equation consists of polynomial terms (squares and products of variables) on both sides.

3. Determine if any operations lead to undefined values. Polynomials are defined for all real numbers because they do not involve division by zero, square roots of negative numbers, or logarithms of non-positive numbers.

4. Conclude the domain. Since there are no constraints on the variables, each variable can be any real number.

Final Answer

Domain: *{(a,b,d,g,h)∈ℝ^5}

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