Home
Class 10
MATHS
If x=3, y=2 and z=-1 , then the value of...

If x=3, y=2 and z=-1 , then the value of `(x^3+y^3+1)/(y^3-z^3)` is

A

4

B

1

C

`-2`

D

0

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \((x^3 + y^3 + 1) / (y^3 - z^3)\) given \(x = 3\), \(y = 2\), and \(z = -1\), we will follow these steps: ### Step 1: Substitute the values of \(x\), \(y\), and \(z\) into the expression. We have: \[ x = 3, \quad y = 2, \quad z = -1 \] Substituting these values into the expression gives: \[ \frac{(3^3 + 2^3 + 1)}{(2^3 - (-1)^3)} \] ### Step 2: Calculate \(x^3\), \(y^3\), and \(z^3\). Calculating each term: \[ 3^3 = 27, \quad 2^3 = 8, \quad (-1)^3 = -1 \] ### Step 3: Substitute the calculated values back into the expression. Now we substitute these values into the expression: \[ \frac{(27 + 8 + 1)}{(8 - (-1))} \] ### Step 4: Simplify the numerator and the denominator. Calculating the numerator: \[ 27 + 8 + 1 = 36 \] Calculating the denominator: \[ 8 - (-1) = 8 + 1 = 9 \] ### Step 5: Write the simplified expression. Now we have: \[ \frac{36}{9} \] ### Step 6: Simplify the fraction. Now we simplify: \[ \frac{36}{9} = 4 \] ### Final Answer: Thus, the value of the expression is \(4\). ---
Promotional Banner

Topper's Solved these Questions

  • FUNDAMENTALS OF ALGEBRA

    MCGROW HILL PUBLICATION|Exercise Multiple Choice Questions|23 Videos
  • FOLDING PAPER CUTTING

    MCGROW HILL PUBLICATION|Exercise EXERCISE|15 Videos
  • HEIGHTS AND DISTANCES

    MCGROW HILL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|41 Videos

Similar Questions

Explore conceptually related problems

If x=1, y=2 and z =3 then find the value of x^3 - z^3 + y^3

If x = 1, y = 2 , z = 5 , find the value of x^3 - y^3 -z^3

If x = 2a- 1, y = (2a - 2) and z =3 - 4a, then the value of x ^(3) + y ^(3) + z ^(3) will be :

If x+y+z=6, then the value of (x-1)^(3)+(y-2)^(3)+(z-3)^(3) is

If x = 1, y = - 2 and z = 3. find the value of (i) x^(3) + y^(3) + z^3-3xyz (ii) 3xy^(4) - 15 x^(2) y + 4z

If A=[(x,y,z),(y,z,x),(z,x,y)] and A^3=I_3 and xyz=2 and x+y+z gt 0 find the value of x^3+y^3+z^3 is

If x + y + z = 6 and x^2 + y^2 + z^2= 20 then the value of x^3 + y^3 + z^3 - 3xyz is

MCGROW HILL PUBLICATION-FUNDAMENTALS OF ALGEBRA-Multiple Choice Questions
  1. The simplified value of the expression (a+b-c)^2+2(a+b-c)(a-b+c)+(a-b+...

    Text Solution

    |

  2. The value of (x-y)^3+(x+y)^3+3(x-y)^2(x+y)+3(x+y)^2(x-y) is

    Text Solution

    |

  3. If p+q=2 , pq=1 then the value of p^3+q^3+6p^2+5q^2+6pq is

    Text Solution

    |

  4. If x-1/x=3, then the value of x^3-1/x^3 is

    Text Solution

    |

  5. If x=3, y=2 and z=-1 , then the value of (x^3+y^3+1)/(y^3-z^3) is

    Text Solution

    |

  6. If a = 15, b = 12 and c= 9, find the value of sqrt(((2a+2b)(2c+a))/(2(...

    Text Solution

    |

  7. If x=40, y=43, z=47 , find the value of x^3+y^3+z^3-3xyz.

    Text Solution

    |

  8. If P varies directly as QR and the values of P, Q. R be 6, 9, 10 repec...

    Text Solution

    |

  9. If (x+a) is a factor of f(x)=x^3+ax^2-2x+a+4 , then a is

    Text Solution

    |

  10. If m is any positive integer, then the last two digits in the expressi...

    Text Solution

    |

  11. If (x-a)/(b+c)+(x-b)/(c+a)+(x-c)/(a+b)=3 then value of x is

    Text Solution

    |

  12. The value of x that satisfies the equation 4/(x-3)+5/(x-5)=9/(x-13) is

    Text Solution

    |

  13. If 0.3x -0.37 = 0.37x -0.3, then x has the value

    Text Solution

    |

  14. If x/6+y/15=4 and x/3-y/12=4 3/4 find x and y.

    Text Solution

    |

  15. If x+y=sqrt3, x-y=sqrt2, then the expression 8xy(x^2+y^2) has the valu...

    Text Solution

    |

  16. In a pair of fractions, fraction A is twice the fraction B and the ...

    Text Solution

    |

  17. The difference between the numerator and the denominator of a fraction...

    Text Solution

    |

  18. A person's present age is 2/5th of the age of his mother. After 8 year...

    Text Solution

    |

  19. Tanya's grandfather was 8 times older to her 16 years ago. He would be...

    Text Solution

    |

  20. A man was asked to state his age in years. his reply was Take my ag...

    Text Solution

    |