Question

if the roots are equal in x square(a square + b square )+ 2( ac+bd) + c square + d square =0,ProveThat ad=bc​

Answer 1

Answer:

( 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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