Home
Class 9
MATHS
If x=1/(2-sqrt(3)), find the value of x^...

If `x=1/(2-sqrt(3)),` find the value of `x^3-2x^2-7x+5`

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of the expression \( x^3 - 2x^2 - 7x + 5 \) given that \( x = \frac{1}{2 - \sqrt{3}} \). ### Step 1: Rationalize \( x \) We start with: \[ x = \frac{1}{2 - \sqrt{3}} \] ...
Promotional Banner

Topper's Solved these Questions

  • QUADRILATERALS

    RD SHARMA|Exercise All Questions|251 Videos
  • SURFACE AREA AND VOLUME OF A CUBOID AND CUBE

    RD SHARMA|Exercise All Questions|168 Videos

Similar Questions

Explore conceptually related problems

If x=2-sqrt(3); find the value of x^(3)-2x^(2)-7x+5

If x=(1)/(2-sqrt(3)) , the value of x^(3)-2x^(2)-7x+10 is equal to

If x=(1)/(sqrt(5)-2) , find the value of x^(3)-3x^(2)-5x+3 .

If x = (1)/(3-sqrt(8)) , find the value of x^(3)- 2x^(2) -78x + 5

If x=(1)/(2+sqrt(3)) of ,find the value 2x^(3)-7x^(2)-2x+1

If x=(sqrt(3)+1)/(2), find the value of 4x^(3)+2x^(2)-8x+7

if x=2-sqrt(3), find the value of (x-(1)/(x))^(3)

If x=(1)/(7+4sqrt(3)), y=(1)/(7-4sqrt(3)) , find the value of 5x^(2)-7xy-5y^(2)

If x=1-sqrt(2), find the value of (x-(1)/(x))^(3)

If x=(1)/(2-sqrt(3)) then find the value of x+(1)/(x)

RD SHARMA-RATIONALISATION -All Questions
  1. If both a and b are rational numbers, find the values of a and b in ea...

    Text Solution

    |

  2. Evaluate : (15)/(sqrt(10)+sqrt(20)+sqrt(40)-sqrt(5)-sqrt(80)), is bein...

    Text Solution

    |

  3. If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

    Text Solution

    |

  4. If x=1-sqrt(2),find the value of (x-1/x)^3

    Text Solution

    |

  5. If x=3-2sqrt(2),find x^2+1/(x^2)

    Text Solution

    |

  6. If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^2-b...

    Text Solution

    |

  7. If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt...

    Text Solution

    |

  8. Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sq...

    Text Solution

    |

  9. Simplify each of the following :3/(5-sqrt(3))+2/(5+sqrt(3))

    Text Solution

    |

  10. If x=2+sqrt(3) , find the value of x^2+1/(x^2)

    Text Solution

    |

  11. Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))+1/(...

    Text Solution

    |

  12. Simplify : (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

    Text Solution

    |

  13. Simplify the following expressions: (3+sqrt(3))(2+sqrt(2))

    Text Solution

    |

  14. Simplify the following: (16)^(1/5)xx(2)^(1/5)

    Text Solution

    |

  15. Simplify the following expressions: (i)(11+sqrt(11))(11-sqrt(11)) ...

    Text Solution

    |

  16. Simplify the following expressions: (4+sqrt(7))(3+sqrt(2))

    Text Solution

    |

  17. Simplify each of the following: (i) 4 3×16 3 (ii) (1250 4)/(2 4)

    Text Solution

    |

  18. Simplify : (sqrt(5)+sqrt(2))^2

    Text Solution

    |

  19. Rationalise the denominator of 2/(sqrt(3)) .

    Text Solution

    |

  20. Simplify the following expressions: (i)(sqrt(3)+sqrt(7))^2 (ii) ...

    Text Solution

    |