If x = y ( + 2 3 ) = z ( - 2 3 ) then x+y+z is equal to

Step-by-step solution

Let x = y ( + 2 3 ) = z ( - 2 3 ) = k . Then x = k , y = k ( + 2 3 ) , and z = k ( - 2 3 ) . Summing these values, x + y + z = k [ + ( + 2 3 ) + ( - 2 3 )] . Using the sum-to-product formula (A + B) + (A - B) = 2 A B , we have ( + 2 3 ) + ( - 2 3 ) = 2 ( 2 3 ) . Since ( 2 3 ) = - 1 2 , the expression becomes 2 (- 1 2 ) = - . Substituting this back into the sum, x + y + z = k [ - ] = k(0) = 0 . Answer: 0