If is the acute angle between the lines represented by the equation x^2 - 3xy + 2y^2 = 0 , then 3 + 2 3 - 2 =

Step-by-step solution

The given equation of the pair of straight lines is x^2 - 3xy + 2y^2 = 0 . Comparing with the standard form ax^2 + 2hxy + by^2 = 0 , we get a = 1 , 2h = -3 , and b = 2 . The acute angle between the lines is given by = | 2 h^2 - ab a + b | . Substituting the values, we get: = | 2 (- 3 2 )^2 - (1)(2) 1 + 2 | = | 2 9 4 - 2 3 | = 2 ( 1 2 ) 3 = 1 3 We need to find the value of 3 + 2 3 - 2 . Dividing the numerator and the denominator by , we get: 3 + 2 3 - 2 Substituting = 1 3 : 3 ( 1 3 ) + 2 3 ( 1 3 ) - 2 = 1 + 2 1 - 2