Let R2 denote R × R. Let S = {(a, b, c) : a, b, c ∈ R and ax2 + 2bxy + cy2 > 0 for all (x, y) ∈ R2 - {(0, 0}}. Then which of the following statements is (are) TRUE ?
For any given (a, b, c) ∈ S, the system of linear equations ax + by = 1 bx + cy = -1 has a unique solution.
For any given (a, b, c) ∈ S, the system of linear equations (a + 1)x + by = 0 bx + (c + 1)y = 0 has a unique solution.
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The Correct Option isB, C, D
Solution and Explanation
The correct option is (B): If \((3,b,\frac{1}{12})\in S\), then |2b| < 1., (C): For any given (a, b, c) ∈ S, the system of linear equations ax + by = 1 bx + cy = -1 has a unique solution. and (D): For any given (a, b, c) ∈ S, the system of linear equations (a + 1)x + by = 0 bx + (c + 1)y = 0 has a unique solution.