Home
Class 11
MATHS
Show that the statement For any real nu...

Show that the statement For any real numbers a and b, `a^2=b^2`implies that `a = b` is not true by giving a counter-example.

Text Solution

Verified by Experts

Let a = 2 and b = – 2, then a and b are real numbers and `a^2` = `b^2`
∵ `a^2` = `(2)^2` = 4, b2 = `(-2)^2` = 4
`a^2` = `b^2` but a ≠ b (∵ 2 ≠ – 2)
Hence, a,b ∈ R and `a^2` = `b^2` ...
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    NCERT|Exercise EXERCISE 14.1|2 Videos

  • MATHEMATICAL REASONING

    NCERT|Exercise EXERCISE 14.2|3 Videos

  • MATHEMATICAL REASONING

    NCERT|Exercise MISCELLANEOUS EXERCISE|7 Videos

  • LINEAR INEQUALITIES

    NCERT|Exercise EXERCISE 6.2|10 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT|Exercise EXERCISE 7.2|5 Videos

Similar Questions

Explore conceptually related problems

For any two real numbers a and b, sqrt((a-b)^2)+sqrt((b-a)^2) is

For any two real numbers a and b,we define a R b if and only if sin^(2)a+cos^(2)b=1. The relation R is

For any whole numbers a, b, c is it true that (a+b)+c=a+(c+b) ? Give reasons.

By giving a counter example,show that the following statement is not true: p: if all the angles of a triangle are equal,then the triangle is an obtuse angled triangle.

By giving a counter example, show that the following statement are not true : The equation x^(2) - 4 = 0 does not have a root lying between 0 and 3.

Let A,B and C be three sets.If A in B and is it true that is it true that ? If not give an example.

Show that A nn B=A nn B implies A=B

By giving a counter-example, show that the following statement is false: p: If all the sides of a triangle are equal, then the triangle is obtuse angled.

If a, b and c are real numbers such that a < b and clt0 , then of the statements which is true?