Learn Ncert All Solutions

from a handpicked tutor in LIVE 1-to-1 classes

from a handpicked tutor in LIVE 1-to-1 classes

# Show that the statement "For any real numbers a and b, a² = b² implies that a = b" is not true by giving a counter-example.

**Solution:**

The given statement can be written as follows. "If a and b are real numbers such that a^{2} = b^{2}, then a = b".

The given statement has to be proved false. For that we need two real numbers a and b such that a^{2} = b^{2} where a ≠ b .

Let a = 1 and b = - 1

Then, a^{2} = 1^{2} = 1 and b^{2} = (- 1)^{2} = 1

Here, a^{2} = b^{2}

However, a ≠ b

Thus, it can be concluded that the given statement is false

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.5 Question 2

## Show that the statement "For any real numbers a and b, a² = b² implies that a = b" is not true by giving a counter-example

**Summary:**

It is proved that the given statement is false

Math worksheets and

visual curriculum

visual curriculum