Question

Question 4 By giving a counter example, show that the following statements are not true.

(i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.

(ii) q: The equation x^2 – 1 = 0 does not have a root lying between 0 and 2.

Class X1 - Maths -Mathematical Reasoning Page 342

Answer 1

(i) obtuse angle is greater than 90° .
Let all angles of Triangle are (90° + α )
then sum of angles of Triangle = (90° + α) + (90° + α ) + (90° + α)
= 270° + 3α

but we know,
sum of angles of any triangle is equal to 180° .
but here (270° + 3α) > 180°

hence, statement is not true .

(ii) x² - 1 = 0
use formula , a² - b² = (a - b)(a + b)
∴ x² - 1² = (x -1) (x + 1) = 0
=> x = -1 , 1
here it is clear that one root x = 1 of equation x²-1 = 0 is lying between 0 to 2.
Hence statement is not true .