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Let a, b, c be any real numbers. Supp...

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""a n d""z""=""b x""+""a y` . Then `a^2+""b^2+""c^2+""2a b c` is equal to (1) 2 (2) `""1` (3) 0 (4) 1

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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""=""c y""+""b z , ""y""=""a z""+""c x"", ""z""=""b x""+""a y . Then a^2+""b^2+""c^2+""2a b c is equal to (1) 2 (2) ""1 (3) 0 (4) 1

Let a,b,c, be any real number. 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^(2)+b^(2)+c^(2) +2abc is equal to

Let z_1, z_2, z_3 be three complex numbers and a ,b ,c be real numbers not all zero, such that a+b+c=0a n da z_1+b z_2+c z_3=0. Show that z_1, z_2,z_3 are collinear.

Let z_1, z_2, z_3 be three complex numbers and a ,b ,c be real numbers not all zero, such that a+b+c=0 and a z_1+b z_2+c z_3=0. Show that z_1, z_2,z_3 are collinear.

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

Show that |a b c a+2x b+2y c+2z x y z|=0

If the system of equations x=c y+b z y=a z+c x z=b x+a y has a non-trivial solution, show that a^2+b^2+c^2+2a b c=1

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

If x , y , z are not all zero such that a x+y+z=0 , x+b y+z=0 , x+y+c z=0 then prove that 1/(1-a)+1/(1-b)+1/(1-c)=1

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y=z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

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