Home
Class 11
MATHS
Prove by direct method that for any real...

Prove by direct method that for any real numbers `x,y` if `x=y`, then `x^(2)=y^(2)`

Text Solution

Verified by Experts

The correct Answer is:
Hence give statement is proved.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    KUMAR PRAKASHAN|Exercise SOLUTION OF NCERT EXEMPLAR PROBLEMS (OBJECTIVE TYPE QUESTIONS)|21 Videos

  • MATHEMATICAL REASONING

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE (Knowledge Test:)|2 Videos

  • MATHEMATICAL REASONING

    KUMAR PRAKASHAN|Exercise TEXT BOOK ILLUSTRATIONS FOR PRACTICE WORK|53 Videos

  • LIMITS AND DERIVATIVES

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for practice work|35 Videos

  • OBJECTIVE SECTION AS PER NEW PAPER SCHEME

    KUMAR PRAKASHAN|Exercise Sequence and Series (Fill in the blanks )|48 Videos

Similar Questions

Explore conceptually related problems

Find counter examples to disprove the following statements: For any integers x and y, sqrt(x^(2) + y^(2)) = x+y

Using direct method prove that if x, y in N and x,y are odd then xy is also odd.

Prove that if x and y are both odd positive Integers, then x^(2) + y^(2) is even but not divisible by 4.

Identify the Quantifiers in the following statements: for all real number x and y ,x.y=y.x

If x, y in R then x+iy is a non-real complex number, if

Show that the family of curves for which the slope of the tangent at any point (x,y) on its (x^(2) + y^(2))/(2xy) , is given by x^(2) - y^(2) = cx .

Prove the statement by the principle of mathematical induction : For any natural numbers n, x^n - y^n is divisible by x - y , where x and y any integers with x ne y

If x , y , z are all different real numbers, then 1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2

Let [a] denotes the larger integer not exceeding the real number a if x and y satisfy the equations y=2[x]+3 and y=3[x-2[ simultaneously determine [x+y]

If z=x+iy , where x and y are real numbers and |x|+|y| lt= k|z| then k=.....

KUMAR PRAKASHAN-MATHEMATICAL REASONING-SOLUTION OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. Write down the converse of following statements: If x:y=3:2 then 2x=...

    Text Solution

    |

  2. Write down the converse of following statements: If S is a cyclic qu...

    Text Solution

    |

  3. Write down the converse of following statements: If x is zero then x...

    Text Solution

    |

  4. Write down the converse of following statements: If two triangles ar...

    Text Solution

    |

  5. Identify the Quantifiers in the following statements: There exists a...

    Text Solution

    |

  6. Identify the Quantifiers in the following statements: for all real n...

    Text Solution

    |

  7. Identify the Quantifiers in the following statements: There exists a ...

    Text Solution

    |

  8. Identify the Quantifiers in the following statements: For every natur...

    Text Solution

    |

  9. Identify the Quantifiers in the following statements: For all real n...

    Text Solution

    |

  10. Identify the Quantifiers in the following statements: There exists a...

    Text Solution

    |

  11. Identify the Quantifiers in the following statements: for all negativ...

    Text Solution

    |

  12. Identify the Quantifiers in the following statements: There exists a ...

    Text Solution

    |

  13. Identify the Quantifiers in the following statements: There exists a ...

    Text Solution

    |

  14. Identify the Quantifiers in the following statements: There exists a...

    Text Solution

    |

  15. Prove by direct method that for any integer n, n^(3)-n is always even.

    Text Solution

    |

  16. Check the validity of the following statement: p:125 is divisible by ...

    Text Solution

    |

  17. Check the validity of the following statement: p:131 is a multiple of...

    Text Solution

    |

  18. Check the validity of the statements given below by the method given a...

    Text Solution

    |

  19. Prove by direct method that for any real numbers x,y if x=y, then x^(2...

    Text Solution

    |

  20. Using contrapositive method prove that if n^(2) is an even integer, th...

    Text Solution

    |