Question
Question: If x, y, z are in A.P. then the value of (x + y – z) (y + z – x) is...
If x, y, z are in A.P. then the value of (x + y – z) (y + z – x) is
A
8yz – 3y2 – 4z2
B
4xz + 3y2
C
8xy + 4x2 – 3y2
D
None of these
Answer
8yz – 3y2 – 4z2
Explanation
Solution
By the given condition
2y = x + z [Q x, y, z are in A.P.]
\ (x + y – z) (y + z –x)
= (2y – z + y – z) (y + z –2y + z)
= (3y –2z) (2z – y) = 8yz –3y2 –4z2