Home
Class 12
MATHS
If a^(2)+b^(2)+c^(2)-2a-4b-6c= -14 then ...

If `a^(2)+b^(2)+c^(2)-2a-4b-6c= -14` then `a+b+c =`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( a^2 + b^2 + c^2 - 2a - 4b - 6c = -14 \), we will follow these steps: ### Step 1: Rearranging the Equation We start by moving \(-14\) to the left side of the equation: \[ a^2 + b^2 + c^2 - 2a - 4b - 6c + 14 = 0 \]
To solve the equation \( a^2 + b^2 + c^2 - 2a - 4b - 6c = -14 \), we will follow these steps: ### Step 1: Rearranging the Equation We start by moving \(-14\) to the left side of the equation: \[ a^2 + b^2 + c^2 - 2a - 4b - 6c + 14 = 0 \]
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

  • TEST SERIES

    RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

Similar Questions

Explore conceptually related problems

If a+b+c=0 and a^2+b^2+c^2=1, then (a) a b+b c+c a=1/2 (b) a b+b c+c a=-1/2 (c) a^4+b^4+c^4=1/2 (d) a^4+b^4+c^4=3/2

Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) (ii) (3x-5y-4)(9x^(2)+25y^(2)+15xy+12x-20y+16) (iii) (2-3b-7c)(4+9b^(2)+49c^(2)+6b-21bc+14c) (iv) (sqrt(2)a+2sqrt(2)b+c)(2a^(2)+8b^(2)+c^(2)-4ab-2sqrt(2)bc-sqrt(2)ac)

If a!=b!=c\ a n d\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 then a+b+c=0 b. a b+b c+c a=0 c. a^2+b^2+c^2=a b+b c+c a d. a b c=0

Factorise : 2ab^(2) c - 2a + 3b^(3) c - 3b - 4b^(2) c^(2) + 4c

If c^2 = a^2 + b^2, 2s = a + b + c , then 4s(s-a) (s - b)(s-c)

If |(a^2,b^2,c^2),((a+1)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

Which of the following is equivalent to (2b^(3)c^(2)+b^(2)c)-(b^(3)c^(2)-b^(2)c-4bc) ?

Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS
  1. If a^(2)+b^(2)+c^(2)-2a-4b-6c= -14 then a+b+c =

    Text Solution

    |

  2. The least positive vlaue of the parameter 'a' for which there exist at...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x + tan x and f si the inverse of g, then g'(x) equals

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. The function f(x) = (x^(2) - 1)|x^(2) - 3x + 3|+cos (|x|) is not diffe...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

    Text Solution

    |

  15. The sum of the roots of the equation tan^(-1)(x+3)-tan^(-1)(x-3)="sin"...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5, find all the points at which the tangents p...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y + b = m(1)(x + a) and y + b = m(2)(x+a) are two tangents to the p...

    Text Solution

    |