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 a² + b² + c² + 2abc is equal to

2

-1

0

1

Solution

The system of equations x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 have non-trivial solution if
$open vertical bar table row 1 cell negative straight c end cell cell negative straight b end cell row straight c cell negative 1 end cell straight a row straight b straight a cell negative 1 end cell end table close vertical bar space equals space 0 space rightwards double arrow space 1 left parenthesis space 1 minus straight a squared right parenthesis space plus space straight c left parenthesis negative straight c minus ab right parenthesis minus straight b left parenthesis ca plus straight b right parenthesis space equals space 0 space rightwards double arrow space straight a squared space plus straight b squared space plus space straight c squared space plus space 2 abc space equals space 1$

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Determinants

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 a² + b² + c² + 2abc is equal to

2

-1

0

1

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Determinants

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 a2 + b2 + c2 + 2abc is equal to 2 -1 0 1

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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 a² + b² + c² + 2abc is equal to

2

-1

0

1