Home
Class 12
MATHS
Consider a equation x^(3)-3x=sqrt(x+2) s...

Consider a equation `x^(3)-3x=sqrt(x+2)` such that `x` is a real number then sum of its positive roots is `lamda` where `[(lamda)/2]` is______

Text Solution

Verified by Experts

The correct Answer is:
1
`implies2cos3theta=sqrt(2(1+costheta))`
`implies2"sin"(7theta)/4."sin"(5theta)/4=0`
`impliestheta=0, (4pi)7, (4pi)/5`
`:. X-2, 2"cos"(4pi)/7, -1.2(1+sqrt(5))`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

If product of the real roots of the equation, x^(2)-ax+30=2sqrt((x^(2)-ax+45)),agt0 is lamda minimum value of sum of roots of the equation is mu . The value of (mu) (where (.) denotes the least integer function) is

Consider an ellipse (x^(2))/25+(y^(2))/16=1 and ABCD be a quadrilateral circumscribing the ellipse. Let S be one of its focii, then /_ASB+/_CSD=(3pi)/(lamda) where lamda is_______

Consider a parabla y^(2)=8x . If PSQ is a focal chord of the parabola whose vertex is A and focus S,V being the middle point of the chord such that PV^(2)=AV^(2)+lamda.AS^(2) where lamda is______

For the equation: x^(2)+18x+30=2sqrt(x^(2)+18x+45) a. product of real root of the equation is 20b . sum of real real root the equation is-18c. product of real root of the equation is 20d . sum of real root of the equation is 18

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

The sum of the real roots of the equation 2x-3=sqrt(2x^(2)-2x+21) is

Let lamdane 0 be in R. If alpha and beta are the roots of the equation x^(2) - x + 2lamda = 0 , and alpha and gamma are the roots of the equation 3x^2 - 10x + 27lamda = 0 , then (betagamma)/lamda is equal to __________

Number of real roots of the equation |3x-2|+|1-x|=sqrt(3-4x) is/are

FIITJEE-TEST PAPERS-MATHEMATICS
  1. For continuous function f: [0, 1]-> R ; A =int0^1 (x^2* f(x))dx ; B=in...

    Text Solution

    |

  2. Let A be an nxxn matrix such that A+A^(')=O(nxxn) then |I+lamdaA^(2)|g...

    Text Solution

    |

  3. Consider a equation x^(3)-3x=sqrt(x+2) such that x is a real number th...

    Text Solution

    |

  4. Consider A and B as 2xx2 matrices with determinant equal to 1 then t...

    Text Solution

    |

  5. Consider an ellipse (x^(2))/25+(y^(2))/16=1 and ABCD be a quadrilatera...

    Text Solution

    |

  6. Consider a parabla y^(2)=8x. If PSQ is a focal chord of the parabola w...

    Text Solution

    |

  7. If alpha in(0,1) and f:R->R and lim(x->oo)f(x)=0,lim(x->oo)(f(x)-f(alp...

    Text Solution

    |

  8. Let f: [a, b] -> R be a function, continuous on [a, b] and twice diff...

    Text Solution

    |

  9. If f(x(1)-x(2)),f(x(1))f(x(2)) & f(x(1)+x(2)) are in A.P. for all x(1)...

    Text Solution

    |

  10. Consider a sequence {an} with a1 =(a(n-1)^2)/(a(n-2)) for all n ge 3 ...

    Text Solution

    |

  11. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...

    Text Solution

    |

  12. Let ABC be a triangle with incentre I. If P and Q are the feet of the ...

    Text Solution

    |

  13. Let hatu, hatv, hatw be three unit vectors such that hatu+hatv+hatw=ha...

    Text Solution

    |

  14. Consider the integral "l"(1)=int(1)^(e)(1+x)(x+Inx)^(100)dx. "l"(2)=in...

    Text Solution

    |

  15. The equation k+x^(3)e^(x+3)=0 has 2 distinct real roots & k is a prime...

    Text Solution

    |

  16. If the equation2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0 has ...

    Text Solution

    |

  17. Equation of the circles |z-1-i|=1 & |z-1+i|=1 touches internally a cir...

    Text Solution

    |

  18. Let a=sin^(-)(sin3)+sin^(-1)(sin4)+sin^(-1)(sin5),f(x)=e^(x^(2)+|x|), ...

    Text Solution

    |

  19. A tosses 2 fair coins & B tosses 3 fair cons after game is won by the ...

    Text Solution

    |

  20. The vertices of a triangle OBC are O(0,0),B(-3,-1),C(-1,-3). Equation ...

    Text Solution

    |