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5. If x, y, z are in AP, then the value of
(x + y - z) (y + z - x) is equal to
(1) Syz - 3y2 - 4z2 (2) Syz - 3z2 - 4y2
(3) Xyz + 3y2 - 4z2
(4) Syz - 3y2 + 4z2
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1
5. If x, y, z are in AP, then the value of
(x + y - z) (y + z - x) is equal to
(1) Syz - 3y2 - 4z2 (2) Syz - 3z2 - 4y2
(3) Xyz + 3y2 - 4z2
(4) Syz - 3y2 + 4z2
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Answer:
Option 1 is correct
Step-by-step explanation:
x,y and z are in AP, then 2y=x+z
Substituting x as 2y−z in the above expression, we get
(x+y−z)(y+z−x)
=(2y−z+y−z)(y+z−2y+z)
=(3y−2z)(−y+2z)
=6yz−3y^2 −4z^2 +2yz
=8yz−3y^2−4z^2