The number of solution pairs (x, y) of the simultaneous equations _ 1 / 3 (x+y)+ ₃(x-y)=2 and 2 y²=512^ x+1 is

Step-by-step solution

array l _ 3⁻¹ (x+y)+ ₃(x-y)=2 - ₃(x+y)+ ₃(x-y)=2 ₃ ( x-y x+y )=2 x-y x+y =9 2^ y² = (2⁹ )^ x+1 2^ y² =2^ 9(x+1) y²=9(x+1) array Solve eliminate y array l 16 x²-225 x-225=0 x=15, -15 16 array At x=15, y=-12x= -15 16 , y= 3 4 (not possible) only sol. x=15, y=-12 only one sol.