Question

if the roots of this equation (a2 + b2)x2 - 2(ac +bd)x + (c2 + d2)=0

are equal prove that a/b =c/d

{plz note: i was trying to put 2 as square and it wasn't working,so all the twos exept the one in b are squares }

Plz help me solving this question

Answer 1

Hey


Given equation is :-


( a² + b² )x² - 2( ac + bd ) + ( c² + d² ) = 0


Now ,

D = 0


So ,

b² - 4 ac = 0


=> [ - 2 ( ac + bd ) ] ² - 4 ( a² + b² ) ( c² + d² ) = 0


=> 4 ( a²c² + b²d² + 2abcd ) - 4 ( a²c² + a²d² + b²c² + b²d² ) = 0


=> 4 [ a²c² + b²d² + 2abcd - a²c² - a²d² - b²c² - b²d² ] = 0


=> 2abcd - a²d² - b²c² = 0


=> a²d² + b²c² - 2abcd = 0


=> ( ad - bc ) ² = 0


=> ac - bd = 0


=> ac = bd


So ,


a / b = c / d


♦ Proved ♦


thanks :)