Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz , y = az + cx and z = bx + ay . Then a - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + b z, y = a z + c x and z = b x + a y . Then a^{2} + b^{2} + c^{2} + 2 ab c is equal to:

Solution & Step-by-step Explanation

The system of equations can be written as: 1 x - cy - b z = 0 - c x + 1 y - a z = 0 - b x - a y + 1 z = 0 For a non-trivial solution (not all zero), the determinant of the coefficients must be zero: 1 - c - b - c 1 - a - b - a 1 = 0 1 (1 - a^{2}) + c (- c - ab) - b (a c + b) = 0 1 - a^{2} - c^{2} - ab c - ab c - b^{2} = 0 1 - a^{2} - b^{2} - c^{2} - 2 ab c = 0 a^{2} + b^{2} + c^{2} + 2 ab c = 1

Try it yourself before checking the explanation above.

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + b z, y = a z + c x and z = b x + a y . Then a^{2} + b^{2} + c^{2} + 2 ab c is equal to:

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