Home
Class 12
MATHS
Given x=cy+bz,y=az+cx and z=bx+ay, then ...

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

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Expansion of Determinant|5 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

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

Given x = cy+bz, y = az + cx, z = b x + ay where, x,y,z are not all zero prove that a^2+b^2 +c^2 + 2 a b c = 1.

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that x^(2) + y^(2) + z^(2) + 2xyz = 1

If y =(ax +b)/( cx + d) , then prove that 2y_1y_3=3(y_2)^2

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

If y = x log (x/(a+bx)) , prove that x^3 y _2 = (xy_1 - y)^2

If y = e^[ax] sin bx , prove that d^2y/dx^2 - 2a dy/dx +(a^2 + b^2 ) y = 0 .

If the planes x-cy-bz=0, cx-y+az=0 and bx+ay-z=0 pass through a line, then the value of a^2+b^2+c^2+2abc is

If f(x)=x^3+bx^2+cx+d and 0< b^2 < c , then

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Given x=cy+bz,y=az+cx and z=bx+ay, then prove a^(2) +b^(2) +c^(2) +2ab...

    Text Solution

    |

  2. If a^2+b^2+c^2=-2, and f(x)= |{:(1+a^2x,(1+b^2)x,(1+c^2)x),((1+a^2)x,...

    Text Solution

    |

  3. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  4. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

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

    Text Solution

    |

  8. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k for which the linear equations 4x+ky+2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |{:((1+...

    Text Solution

    |

  16. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

    Text Solution

    |

  17. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  18. Let a, lambda , mu in R.Consider the system of linear equations ax...

    Text Solution

    |

  19. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |