Show that if roots of equation (a^2...
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Show that if roots of equation ( left(a^{2}-b cright) x^{2}+2left(b^{2}-a cright) x+c^{2}-a b=0 ) are equal, then either ( b=0 ) or ( a^{3}+b^{3}+c^{3}=3 a b c )

IIT/JEE
Physics
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Show that if roots of equation (a^2−bc)x^2+2(b^2−ac)x+c^2−ab=0 are equal, then either b=0 or a^3+b^3+c^3=3abc
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( D=0 )
( left(2left(b^{2}-a cright)right)^{2}-4left(a^{2}-b cright)left(c^{2}-9 bright)=0 )
( 4left(left[b^{2}-9 cright)^{2}-left(a^{2}-6 cright)left(c^{2}-a bright)right]=0 )
( 6^{4}+9^{2} c^{2}-29 b^{2} c-left(9^{2} c^{2}-6 c^{3}-9^{3} b+9 b^{2} c^{2}right) )
( =0 )
( 6^{4}+9^{2} k^{2}-29 b^{2} c-9^{2} c^{2}+6 c^{3}+9^{3} b^{2} c= )
( 6left(6^{3}-396 c+9^{3}+c^{3}right)=0 )
then ( 6=0 ) of ( a^{3}+b^{3}+c^{3}-3 a b c )

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