Question

If x,y,z are in A.P. then the value of (x+y-z)(y+z-x) is A]8yz - 3y^2 -4z^2 B]4xz -3y^2 C]8xy- 4x^2 -3y^2 D]10xz- 3x^2 -3z^2 URGENT

Answer 1

Answer :

Given 

x , y , z​ are in A.P. 
And we know common difference will be same if some numbers are in A.P.
So,

y  - x  = z  - y 

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

now we have

( x + y  - z ) ( y  + z​  - x ) 

we can write it As :

( x + y  + z - 2z ) ( x + y  + z​  - 2x ) 

Substitute value from equation 1 and get 

⇒( 2y + y  - 2z ) ( 2y + y  ​  - 2x )

⇒( 3y - 2z ) ( 3y - 2x )

⇒9y2 - 6xy - 6yz + 4xz 

⇒9y2 - 6y ( x + z ) + 4xz 

⇒ 9y2 - 6y ( 2y ) + 4xz ​                                            ( from equation 1 we know 2y = x + z​ ​ )

⇒9y2 - 12y2 + 4xz ​ 

⇒4xz  - 3y2 



 

Answer 2

the answer above is wrong.....it's in u like 2018-19 model test paper 7 , question 2 and it's answer is given 8yz-3y2-4z2........
2 means square here