Home
Class 11
MATHS
Show that for any triangle with sides a ...

Show that for any triangle with sides `a ,b ,and c, 3(a b+b c+c a)<(a+b+c)^2<4(b c+c a+a b)dot` When are the first two expressions equal ?

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

In Delta ABC, a, b and A are given and c_(1), c_(2) are two values of the third side c. Prove that the sum of the area of two triangles with sides a, b, c_(1) and a, b c_(2) " is " (1)/(2) b^(2) sin 2A

If Delta is the area of a triangle with side lengths a, b, c, then show that as Delta leq 1/4 sqrt((a + b + c) abc) Also, show that the equality occurs in the above inequality if and only if a = b = c .

Using determinant : show that the area of the triangle with vertices at (a^2,a^3),(b^2,b^3)and (c^2,c^3) is 1/2(a-b)(b-c)(c-a)(ab+bc+ca) square unit.

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

Show that none of the following sentences is a statement : a , b , c are the lenghts of the sides of a triangle .

In any triangle ABC, show that (a sin C)/(b - a cosC)= tanA .

If A,B,C are the angles of a triangle, show that, (i) sin B cos(C +A) + cos B sin (C +A) = 0

If A,B,C are the angles of a triangle, show that, (ii) tan ((A - B)/2) = cot (C/2 + B) .

If x,y,z are the perpendiculars from the vertices of a triangle ABC on the opposite sides a,b,c respectively, then show that (bx)/c+(cy)/a+(az)/b=(a^2+b^2+c^2)/(2R)

If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >2/3 (b) b/c >1/3 b/c<2 (d) b/c<3/2

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x ,y in R a n d2x^2+6x y+5y^2=1,t h e n a. |x|lt=sqrt(5) b. |x|ge...

    Text Solution

    |

  2. If the roots x^5-40 x^4+P x^3+Q x^2+R x+S=0 are n G.P. and the sum of ...

    Text Solution

    |

  3. Show that for any triangle with sides a ,b ,and c, 3(a b+b c+c a)<(a+b...

    Text Solution

    |

  4. For what values of m, does the system of equations 3x+my=m and 2x-5y=2...

    Text Solution

    |

  5. Show that the square to (sqrt(26-15sqrt(3)))//(5sqrt(2)-sqrt(38+5sqrt(...

    Text Solution

    |

  6. If alpha,beta are the roots x^2+px+q=0 and gamma,delta are the roots o...

    Text Solution

    |

  7. Let f(x) =x^2+bx+c, where b,c inR. If f(x) is a factor of both x^4+6x^...

    Text Solution

    |

  8. If the equation a x^2+b x+c=x has no real roots, then the equation a(a...

    Text Solution

    |

  9. The value of expression x^4-8x^3+18 x^2-8x+2 when x=2+sqrt(3) a. 2 ...

    Text Solution

    |

  10. The exhaustive set of values of a for which inequation (a -1)x^2- (a+1...

    Text Solution

    |

  11. If p ,q ,r ,s are rational numbers and the roots of f(x)=0 are eccentr...

    Text Solution

    |

  12. If |z-(1/z)|=1, then a. (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(s...

    Text Solution

    |

  13. zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos th...

    Text Solution

    |

  14. If a0, a1, a2, a3 are all the positive, then 4a0x^3+3a1x^2+2a2x+a3=0 ...

    Text Solution

    |

  15. If 1,z1,z2,z3,.......,z(n-1) be the n, nth roots of unity and omega b...

    Text Solution

    |

  16. If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of poi...

    Text Solution

    |

  17. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |

  18. If the equation z^3 + (3 + i)(z^2) - 3z - (m + i)= 0, m in R , has at ...

    Text Solution

    |

  19. If a+b+c=0,a^2+b^2+c^2=4,t h e na^4+b^4+c^4 is.

    Text Solution

    |

  20. Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...

    Text Solution

    |