Question

If x + z = 2y and b2 = ac, then show that ay – z . bz – x . cx – y = 1.​

Answer 1

Step-by-step explanation:

x + z = 2y-----(1)

x-y=y-z-----(2)

b² = ac --( 3 )

LHS= a^(y-z) xb^(z - x) x c^(x - y)

= a^(x - y) x b^(z - x) x c^(x- y)

[from (2)]

= (ac)^( x - y) x b^(z - x)

= (b²)^(x - y) x b^ (z-x)

[From (3)]

= b^(2x - 2y) * b^(z - x)

= b^(2x - 2y +z - x)

= b^(x + z-2y)

= b^(2y-2y)

[From (1)]

= b^0

= 1

= RHS