Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x=c y+b z, y=a z+c x and z=b x+a y then a2+b2+c2+2 a b c is equal to

Question

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x=c y+b z, y=a z+c x and z=b x+a y then a2+b2+c2+2 a b c is equal to (A) 2° (B) 1 (C) 0 (D) -1

Tardigrade Admin · Accepted Answer

The equation system x - cy - bz = 0 cx - y + az = 0 bx + ay - z = 0 have non trivial solution if |1 - c - b c -1 a b a -1|=0 text Expand by R1, 1(1-a2)+c(-c-a b)-b(a c+b)=0 1-a2-c2-a b c-a b c-b2=0 a2+b2+c2+2 a b c=1

Q. 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

$2^{\circ}$

1

0

-1

Q. 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

The equation system x−cy−bz=0 cx−y+az=0 bx+ay−z=0 have non trivial solution if ∣∣​1cb​−c−1a​−ba−1​∣∣​=0 Expand by R1​,1(1−a2)+c(−c−ab)−b(ac+b)=0 1−a2−c2−abc−abc−b2=0 a2+b2+c2+2abc=1

Q. 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

$2^{\circ}$