Suppose ' a ' and ' b ' are non-zero constants satisfying the following system of equations a ^3 x + b ^3 x = x x and a x - b x = 0 , then 2(a^6 + b^6) - 3(a^4 + b^4) + 1 =

Step-by-step solution

Given the equation a x - b x = 0 , we have a x = b x . Substitute b x = a x into the first equation a ^3 x + b ^3 x = x x : a x ^2 x + (b x) ^2 x = x x a x ^2 x + a x ^2 x = x x a x ( ^2 x + ^2 x) = x x a x = x x Since a and b are non-zero constants, x 0 . Dividing by x , we get a = x . Similarly, substituting a x = b x into the first equation gives: (a x) ^2 x + b ^3 x = x x b x ^2 x + b x ^2 x = x x b x ( ^2 x + ^2 x) = x x b x = x x Dividing by x , we get b = x . Therefore, a^2 + b^2 = ^2 x + ^2 x = 1 . Now, eva