Math miscellaneousEasy
Question
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
Options
A.2
B.-1
C.0
D.1
Solution
The system of equations x - cy - bz = 0, cx - y + az = 0 and bx + ay - z = 0 have non-trivial solution if
= 0 ⇒ 1(1 - a2) + c(-c - ab) - b(ca + b) = 0
⇒ a2 + b2 + c2 + 2abc = 1.
= 0 ⇒ 1(1 - a2) + c(-c - ab) - b(ca + b) = 0⇒ a2 + b2 + c2 + 2abc = 1.
Create a free account to view solution
View Solution FreeMore Math miscellaneous Questions
Let f(x) Then which one of the following is true?...The lines p(p2 + 1) x - y + q = 0 and (p2 + 1)2 x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for...If | a |=5, | b | = 4, | c | = 3 thus what will be the value of | a.b + b.c + c.a |, given that = 0...The variance of first 50 even natural numbers is...The value of|1 - x2|dx is...