If is the acute angle between the lines 2x^2 + 7xy + 3y^2 = 0 , then the value of 2 - 3 4 + 5 =

Step-by-step solution

Given equation of the pair of straight lines is 2x^2 + 7xy + 3y^2 = 0 . Comparing with ax^2 + 2hxy + by^2 = 0 , we get a = 2 , h = 7 2 , and b = 3 . The acute angle between the lines is given by: = | 2 h^2 - ab a + b | = | 2 ( 7 2 )^2 - (2)(3) 2 + 3 | = | 2 49 4 - 6 5 | = | 2 25 4 5 | = 2 5 2 5 = 1 We need to find the value of 2 - 3 4 + 5 . Dividing the numerator and the denominator by , we get: 2 - 3 4 + 5 Substituting = 1 : 2 - 3(1) 4(1) + 5 = -1 9 = - 1 9 Answer: - 1 9