Home
Class 12
MATHS
Evaluate the expression (i) 4x^(3)+2x^...

Evaluate the expression
`(i) 4x^(3)+2x^(2)-8x+7` for `x=(1)/(2)(sqrt(3)+1)`
`(ii) 3x^(2)+4xy-3y^(2)` for `x=(sqrt(5)+sqrt(2))/(sqrt((5))-sqrt((2)))`, `y=(sqrt(5)-sqrt(2))/(sqrt((5))+sqrt((2)))`
`(iii) x^(2)+xy+y^(2)` for `x=(sqrt(3)-sqrt(2))/(sqrt((3))+sqrt((2)))` , `y=(sqrt(3)+sqrt(2))/(sqrt((3))-sqrt((2)))`.

Text Solution

Verified by Experts

The correct Answer is:
(i) 10
(ii)`(1)/(3)[12+56sqrt(10)]`
(iii) 99
Promotional Banner

Topper's Solved these Questions

  • LOGARITHMS AND SURDS

    ML KHANNA|Exercise Problem Set (5) (Multiple choice questions)|10 Videos

  • LOGARITHMS AND SURDS

    ML KHANNA|Exercise Self Assessment test|10 Videos

  • LOGARITHMS AND SURDS

    ML KHANNA|Exercise Problem Set (3) (Multiple choice questions)|15 Videos

  • LINEAR PROGRAMMING

    ML KHANNA|Exercise Self Assessment Test|8 Videos

  • MATHEMATICAL REASONING

    ML KHANNA|Exercise PROBLEM SET (2) ASSERTION/REASON|3 Videos

Similar Questions

Explore conceptually related problems

x=(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)) and y=(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)) then find x^(2)+y^(2)=?

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) find x^(2)+y^(2)

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)), find x^(2)+y^(2)

If x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))"and"y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) then x^2+xy+y^2=

If x=(sqrt(5)-sqrt(2))/(sqrt(5)+sqrt(2)) and y=(sqrt(5)+sqrt(2))/(sqrt(5)-sqrt(2)), find the value of x^(2)-y^(2)

(2)/(sqrt(3)+sqrt(5))+(5)/(sqrt(3)-sqrt(5))=x sqrt(3)+y sqrt(5)

If x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) and y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) then the value of x^(2)+xy+y^(2)

If x=(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)),y=(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)) find the value of (x-y)^(2)

If x=((sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))) and y=((sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))), find the value of (x^(2)+y^(2))

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)), then find the value of x^(2)+y^(2)

ML KHANNA-LOGARITHMS AND SURDS-Problem Set (4)
  1. Take factors outside the radical sign (i) root3(54(1-sqrt(5))^(3)) (...

    Text Solution

    |

  2. Which of the given numbers is greatest ? 6root3(5), root3(2),2root3(...

    Text Solution

    |

  3. Evaluate the expression (i) 4x^(3)+2x^(2)-8x+7 for x=(1)/(2)(sqrt(3)...

    Text Solution

    |

  4. If x = (2ab)/(b^2+1) then value of (sqrt(a+x)+sqrt(a-x))/(sqrt(a+x)-sq...

    Text Solution

    |

  5. If x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b)), then find the va...

    Text Solution

    |

  6. Express as an equivalent fraction with rational denominator. (8sqrt(...

    Text Solution

    |

  7. Express as an equivalent fraction with rational denominator. (11)/(2...

    Text Solution

    |

  8. Express as an equivalent fraction with rational denominator. (sqrt(1...

    Text Solution

    |

  9. Simplify ((sqrt3+sqrt5)(sqrt5+sqrt2))/(sqrt2+sqrt3+sqrt5)

    Text Solution

    |

  10. Express as an equivalent fraction with rational denominator. (1)/(2-...

    Text Solution

    |

  11. Express as an equivalent fraction with rational denominator. (1)/(sq...

    Text Solution

    |

  12. Express as an equivalent fraction with rational denominator. (15)/(s...

    Text Solution

    |

  13. Express as an equivalent fraction with rational denominator. (i) (3+...

    Text Solution

    |

  14. Express as an equivalent fraction with rational denominator. (sqrt(2...

    Text Solution

    |

  15. Express as an equivalent fraction with rational denominator. ([sqrt(...

    Text Solution

    |

  16. (12)/( 3+ sqrt(5 ) + 2sqrt(2)) is equal to

    Text Solution

    |

  17. Prove the following identities. ((a+2)^(2)(a-3)+(a^(2)-4)sqrt(a^(2)-...

    Text Solution

    |

  18. Prove the following identities. (n^(3)-3n+(n^(2)-1)sqrt(n^(2)-4)-2)/...

    Text Solution

    |

  19. Express with rational denominator : (4)/(root3((9))-root3(3)+1)

    Text Solution

    |

  20. Express with rational denominator : (sqrt(8)+root3(4))/(sqrt((8))-ro...

    Text Solution

    |