if the roots of the equation (a²+b²) x²-2 (ac+bd) x +(c²+d²)=0 are equal proven that a/d=c/d
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( a² + b²)x² -2( ab + cd)x +( c² + d²) = 0
roots are equal so, D = b² -4ac =0
{2(ab + cd)}² -4(a² +b²)(c² + d²) =0
4(ab+ cd)² -4(a² + b²)(c²+ d²) =0
( a²b²+c²d² +2abcd ) -a²c²-a²d²-b²d² -b²c² =0
-a²c² -b²d² + 2abcd =0
-( a²c² + b²d² -2abcd) =0
{(ac-bd)²} =0
ac -bd =0
ac = bd
a/b = d/c
hence proved /////
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