if x,y,z are in AP then show that the following are also on AP:
(y+z)²-x²,(z+x)²-y²,(x+y)-z²
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(y+z)² - x²,(z+x)² - y²,(x+y)² - z² are in A.P.
= (x+y+z)(y+z-x) , (x+y+z)(z+x-y) , (x+y+z)(x+y-z) are in A.P.
= y+z-x , z+x-y , x+y-z are in A.P.
= (y+z-x)-(x+y+z) , (z+x-y)-(x+y+z) , (x+y-z)-(x+y+z) are in A.P.
= -2x , -2y , -2z in A.P.
=x , y , z are in A.P. Hence Proved
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