Home
Class 9
MATHS
Prove that : (0. 87xx0. 87xx0. 87+0. 13x...

Prove that : `(0. 87xx0. 87xx0. 87+0. 13xx0. 13xx0. 13)/(0. 87xx0. 87-0. 87xx0. 13+0. 13xx0. 13)=1`

Text Solution

Verified by Experts

`(0.87xx0.87xx0.87+0.13xx0.13xx0.13)/(0.87xx0.87-0.87xx0.13+0.13xx0.13)`
`=((0.87)^3+(0.13)^3)/((0.87)^2-0.87xx0.13+(0.13)^2)`
`=(a^3+b^3)/(a^2-ab+b^2)`
`=((a+b)(a^2-ab+b^2))/(a^2-ab+b^2)`
`=(a+b)`
`=0.87+0.13=1`
Hence proved
`(0. 87xx0. 87xx0. 87+0. 13xx0. 13xx0. 13)/(0. 87xx0. 87-0. 87xx0. 13+0. 13xx0. 13)=1`
Promotional Banner

Topper's Solved these Questions

  • EXPONENTS OF REAL NUMBER

    RD SHARMA|Exercise All Questions|186 Videos

  • FACTORIZATION OF POLYNOMIAL

    RD SHARMA|Exercise All Questions|220 Videos

Similar Questions

Explore conceptually related problems

Prove that (0.85xx 0.85xx 0.85 +0.15xx 0.15xx 0.15)/(0.85xx 0.85-0.85xx 0.15+0.15xx 0.15)=1 .

Prove that (0.85xx0.85xx0.85+0.15xx0.15xx0.15)/(0.85xx0.85-0.85xx0.15+0.15xx0.15)=1

The value of (0.57xx0.57xx0.57+0.43xx0.43xx0,43)/(0.57xx0,57-0.57xx0.43+0.43xx0,43)

(0.7xx0.05xx0.004)/(0.07xx0.04)=

(0.86 xx 0. 86 xx 0. 86 + 0. 14 xx0.14 xx 0. 14)/(0.86 xx 0.86 - 0. 86 + 0.14 + 0.14 xx 0. 14) is equal to

Prove : (87xx87xx87+13xx13xx13)/(87xx87-87xx13+13xx13) =100

RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. Factorize : 27 a^3+1/(64 b^3)+(27a^2)/(4b)+(9a)/(16 b^2)

    Text Solution

    |

  2. Simplify: (x+y)^3-(x-y)^3-6y(x^2-y^2)

    Text Solution

    |

  3. Prove that : (0. 87xx0. 87xx0. 87+0. 13xx0. 13xx0. 13)/(0. 87xx0. 87-0...

    Text Solution

    |

  4. Factorize each of the following expressions : 54 x^6y+2x^3y^4, 8x^...

    Text Solution

    |

  5. Factorize each of the following expressions : x^(12)-y^(12) (ii) x^9-...

    Text Solution

    |

  6. Factorize : (i)x^3+3x^2+3x-7 (ii)x^3-3x^2+3x+7 (iii) x^6-7x^3-8

    Text Solution

    |

  7. Factorize : (i)(x+1)^3 (ii) (x+1)^3+(x-1)^3 (iii) 8(x+y)^3-27(x-y)^3

    Text Solution

    |

  8. Factorize each of the following expressions : (i)a^6-b^6 (ii) a^6+b^6...

    Text Solution

    |

  9. Factorize each of the following expressions by splitting the middle ...

    Text Solution

    |

  10. What are the possible expression for the dimensions of a cuboid whose ...

    Text Solution

    |

  11. If p=2-a , prove that a^3+6a p+p^3-8=0

    Text Solution

    |

  12. Factorize the following expression : (2x-3y)^3+(...

    Text Solution

    |

  13. Factorize : (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3

    Text Solution

    |

  14. Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3

    Text Solution

    |

  15. 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

    |

  16. Find the value of x^3-8y^3-36 x y-216 , when x=2y+6.

    Text Solution

    |

  17. Factorize the following expression : x^4+x^2+1

    Text Solution

    |

  18. Factorize each of the following expressions: 2p(a-b)+3q(5a-5b)+4r(2a...

    Text Solution

    |

  19. Prove that : (a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)=2(a^3+b^3+c^3-3a...

    Text Solution

    |

  20. Factorize the following expression: 4a^2+12 a b+9b^2-8a-12 b

    Text Solution

    |