Let C ( α , β ) be the circumcentre of the triangle formed by the lines 4 x + 3 y = 69 , 4 y - 3 x = 17 , and x + 7 y = 61 . Then ( α - β ) 2 + α + β is equal to

Step-by-step solution

Given, C ( α ,   β ) be the circumcentre of the triangle formed by the lines 4 x + 3 y = 69 , 4 y - 3 x = 17 , and x + 7 y = 61 , Now plotting the diagram of the above equations and finding the intersection point we get, Now from diagram we can see that it is a right-angled triangle, so the circumcentre is given by midpoint of the hypotenuse, Hence, circumcentre will be, C 12 + 5 2 , 7 + 8 2 ⇒ C 17 2 , 15 2 = ( α , β ) Hence, ( α - β ) 2 + α + β = 17 2 - 15 2 2 + 1