If 5 , 5 r , 5 r 2 are the lengths of the sides of a triangle, then r can not be equal to:

Step-by-step solution

Given, 5 ,   5 r ,   5 r 2 are the length of sides of triangle, then we know that the sum of two sides of a triangle is more than the third side i.e. 5 + 5 r > 5 r 2       . . . 1 5 + 5 r 2 > 5 r       . . . 2 5 r + 5 r 2 > 5         . . . 3 From 1 , r 2 - r - 1 < 0 r - 1 + 5 2   r - 1 - 5 2   < 0 r ∈ 1 - 5 2 , 1 + 5 2         . . . 4 from 2 , r 2 - r + 1 > 0 The discriminant of the quadratic is D