Home
Class 9
MATHS
If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^...

If `x^4+1/(x^4)=194 ,` find `x^3+1/(x^3),x^2+1/(x^2)` and `x+1/x`

Text Solution

Verified by Experts

`x^4 + 1/x^4 = 194`
Adding `2(x^2 × 1/x^2)` on both sides,
`x^4 + 1/x^4 + 2(x^2 xx 1/x^2) = 194 + 2(x × 1/x)`
`(x^2 + 1/x^2)^2 = 196`
`x^2 + 1/x^2 = sqrt(196)`
`x^2 + 1/x^2 = 14`
Now,
Adding `2(x xx 1/x)` on both sides,
`x^2 + 1/x^2 + 2(x xx 1/x) = 14 + 2(x xx 1/x)`
`(x + 1/x)^2 = 14 + 2`
`x + 1/x = sqrt(16)=4`
Therefore,
`x^3+ 1 / x^3 = ( x + 1 /x )(x^2 + 1/x^2 - 1 )`
`=4 xx ( 14 - 1 )`
`= 4 xx 13`
`= 52`
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    RD SHARMA|Exercise All Questions|205 Videos

Similar Questions

Explore conceptually related problems

If x+(1)/(x)=4 , then find x^(3)+(1)/(x^(3))

If x+1/(x)=4 and x^2+1/(x^3)=30 then x^3+1/x^2=?

If x^(4)+(1)/(x^(4))=194 . Find the value of (x^(3)+(1)/(x^(3))) .

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))

If x^(2)+(1)/(x^(2))=(17)/(4), then find x-(1)/(x),x+(1)/(x),x^(3)-(1)/(x^(3)) and x^(3)+(1)/(x^(3))

If x-1/x=8 then find x^2+1/x^2 and x^4+1/x^4

If x+(1)/(x)=6, find x^(2)+(1)/(x^(2))( ii) x^(4)+(1)/(x^(4))

If x-1/x=5 , find the value x^(2)+1/(x^(2)) and x^(4)+1/(x^(4))

If x-(1)/(x)=3, find the values of x^(2)+(1)/(x^(2)) and x^(4)+(1)/(x^(4))

RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If x^3+1/(x^3)=110 , then x+1/x=? (a)5 (b) 10 (c) 15 (d) none of ...

    Text Solution

    |

  2. If x^3-1/(x^3)=14 , then x-1/x=? (a)5 (b) 4 (d) 3 (d) 2

    Text Solution

    |

  3. If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^2+1/(x^2) and x+1/x

    Text Solution

    |

  4. If x-1/x=(15)/4, then x+1/x\ =? (a)4 (b) (17)/4 (c) (13)/4\ (d...

    Text Solution

    |

  5. If 3x+2/x=7, then (9x^2-4/(x^2))=? (a)25 (b) 35 (c) 49 (d) 30

    Text Solution

    |

  6. If a^2+b^2+c^2-a b-b c-c a=0, then a+b=c b+c=a c+a=b a=b=c

    Text Solution

    |

  7. If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) ...

    Text Solution

    |

  8. If a^(1/3)+\ b^(1/3)+\ c^(1/3)=0 then (a)a+b+c=0 (b) (a+b+c)^3=27\ a...

    Text Solution

    |

  9. If a+b+c=9 and a b+b c+c a=23 , then a^2+b^2+c^2=? (a)35 (b) 58 (c)...

    Text Solution

    |

  10. If a+b+c=9 and a b+b c+c a=23 , then a^3+b^3+c^3-3a b c=? (a)108 (b) ...

    Text Solution

    |

  11. (a-b)^3 + (b-c)^3 + (c-a)^3=? (a)(a+b+c)(a^2+b^2+c^2-ab-bc-ac) (b)3(...

    Text Solution

    |

  12. Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)...

    Text Solution

    |

  13. The product (a+b)(a-b)(a^2-a b+b^2)(a^2+a b+b^2) is equal to: (a)a^6+b...

    Text Solution

    |

  14. If a/b+b/a=\ -1, then a^3-b^3=? (a)1 (b) -1 (c) 1/2 (d) 0

    Text Solution

    |

  15. The product (x^2-1)(x^4+x^2+1) is equal to: (a)x^8-1 (b) x^8+1 (...

    Text Solution

    |

  16. If a-b=-8\ \ a n d\ \ a b=-12 , then a^3-b^3=? (a)-244 (b) -240 ...

    Text Solution

    |

  17. If the value of a cuboid is 3x^2-27 , then its possible dimensions ar...

    Text Solution

    |

  18. If a/b+b/a=1, then a^3+b^3=? (a)1 (b) -1 (c) 1/2 (d) 0

    Text Solution

    |

  19. 75 \xx\ 75-2 \xx\ 75 \xx\ 25+25 \xx\ 25 is equal to=? (a)10000       ...

    Text Solution

    |

  20. (x−y)(x+y)(x^2+y^2)(x^4+y^4) is equal to=

    Text Solution

    |