# If roots of the equation (a²+b²)x²-2(ac+bd)x+(c²+d²)=0 are equal then prove that a/b=c/d

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by Rau789

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by Rau789

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⇒ [-2(ac + bd)]^2 - 4 x (a^2 + b^2) (c^2 + d^2) = 0

⇒ 4[(ac)^2 + 2abcd + (cd)^2] - 4[(ac)^2 + (ad)^2 + (bc)^2 + (cd)^2] = 0

⇒ [(ac)^2 + 2abcd + (cd)^2] - [(ac)^2 + (ad)^2 + (bc)^2 + (cd)^2] = 0

⇒ (2abcd - (bc)^2 - (ad)^2) = 0

⇒ (bc)^2 - 2abcd + (ad)^2 = 0

⇒ (bc-ad)^2 = 0

⇒ (bc = ad

⇒ a/b = c/d