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

  • -18

I think if it will be b2 then it is possible.

  • -52

 It is given:

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

To prove:

a / b = c / d

PROOF:

we know that

D = b2 - 4ac

b2 = 4ac

{-2(ac + bd) } = 4{(a2 + b2) (c2 + d2)}

4(a2c2 + b2d2 +2acbd) = 4(a2c2 + a2d2 + b2c2 + b2d2)

2acbd = a2d2 + b2c2

a2d2 + b2c2 - 2abcd = 0

(ad - bc)2 = 0

ad - bc = 0 

ad = bc

a / b = c / d

hence proved

  • 57

 It is given:

(a+ b2)x2 - 2(ac+bd)x + (c2 + d2) = 0

To prove:

a / b = c / d

PROOF:

we know that

D = b2 - 4ac

b2 = 4ac

{-2(ac + bd)}2 = 4{(a2 + b2) (c2 + d2)}

4(a2c2 + b2d2 +2acbd) = 4(a2c2 + a2d2 + b2c2 + b2d2)

2acbd = a2d+ b2c2

a2d2 + b2c2 - 2abcd = 0

(ad - bc)2 = 0

ad - bc = 0

ad = bc

a / b = c / d

hence proved.

  • 244
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