Home
Class 12
MATHS
Let a,b,c, be any real number. Suppose t...

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

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Given x=cy+bz,y=az+cx and z=bx+ay, then prove a^(2) +b^(2) +c^(2) +2abc =1.

Prove by direct method that for any real numbers x,y if x=y , then x^(2)=y^(2)

Let a ,ba n dc be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

If z=x+iy , where x and y are real numbers and |x|+|y| lt= k|z| then k=.....

If a, b, c are three positive real numbers such that abc^(2) has the greatest value (1)/(64) , then

If x,y and z are three real numbers such that x+y+z=4 and x^2+y^2+z^2=6 ,then show that each of x,y and z lie in the closed interval [2/3,2]

Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the equation |a x-b y-c b x-a y c x+a b x+a y-a x+b y-cc y+b c x+a c y+b-a x-b y+c|=0 represents a straight line.

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbeta,w h e r ealpha >1 , then show that 1+c/a+|b/a|<0

a and b are real numbers between 0 and 1 such that the points Z_1 =a+ i , Z_2=1+ bi , Z_3= 0 form an equilateral triangle, then a and b are equal to

ALLEN -DETERMINANTS-All Questions
  1. The system of equations ax+y+z=a-1,x+ay+z=a-1andx+y+az=a-1 does not h...

    Text Solution

    |

  2. If D=|[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]| for x!=0, y!=0 then D is (1...

    Text Solution

    |

  3. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  4. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

    Text Solution

    |

  5. Consider the system of linear equations; x1 +2x2+x3=3 2x1+3x2+x3=3 3x1...

    Text Solution

    |

  6. The number of value of k for which the linear equations 4x+k y+2z=0,k ...

    Text Solution

    |

  7. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  8. The number of values of k, for which the system of equations (k""+""...

    Text Solution

    |

  9. If a ,b ,c are sides of a scalene triangle, then value of {:|(a, b, c)...

    Text Solution

    |

  10. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

    Text Solution

    |

  11. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

    Text Solution

    |

  12. Consider the system of equations x+a y=0,\ y+a z=0\,z+a x=0.\ Then th...

    Text Solution

    |

  13. If f(n)=alpha^n+beta^n then show that |{:(3,1+f(1),1+f(2)),(1+f(1),...

    Text Solution

    |

  14. The set of all values of lamda for which the system of linear equation...

    Text Solution

    |

  15. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

    Text Solution

    |

  16. The number of distinct real roots of the equation |cosx s in x s in x ...

    Text Solution

    |

  17. Test the consistency and solve them when consistent the following s...

    Text Solution

    |

  18. If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab...

    Text Solution

    |

  19. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  20. The value of lambda for which the system of equations 2x-y-2z=2,x-2y +...

    Text Solution

    |