The smallest positive value of x in degrees satisfying the equation (x+100^ )= (x+50^ ) (x) (x-50^ ) is

Step-by-step solution

aligned & (x+100^ )= (x+50^ ) (x) (x-50^ ) & (x+100^ ) (x-50^ ) = (x+50^ ) (x) & 2 (x+100^ ) (x-50^ ) 2 (x+100^ ) (x-50^ ) aligned = 2 (x+50^ ) x 2 (x+50^ ) x (2 x+50)+ 150^ (2 x+50)- 150^ = (50^ )- (2 x+50^ ) (2 x+50^ )+ 50^ By componendo-dividendo, we get aligned & 2 (2 x+50^ ) 2 (150^ ) = 2 50^ -2 (2 x+50^ ) & 2 (2 x+50^ ) (2 x+50^ ) & =-2 (150^ ) (50^ ) & (4 x+100^ )=- 50^ & (4 x+100^ )= (270^ -50^ ) & 4 x+100^ =220^ & 4 x=120^ & x=30^ aligned