Question

solve for x: x²-2(a²+b²)x+(a²-b²)=0​

Answer 1

Answer:

Given equation is:

(1 + m 2) x 2 + 2mcx + (c 2 – a 2) = 0

To prove: c 2 = a 2 (1 + m 2)

Proof: It is being given that equation has equal roots, therefore

D = b 2 – 4ac = 0 ... (1)

From the above equation, we have

a = (1 + m 2)

b = 2mc

and c= (c 2 – a 2)

Putting values of a, b and c in (1), we get

D = (2mc)2 – 4 (1 + m 2) (c 2 – a 2) = 0

⇒ 4m 2 c 2 – 4 (c 2 + c 2 m 2 – a 2 – a 2 m 2) = 0

⇒ 4m 2 c 2 – 4c 2 – 4c 2 m 2 + 4a 2 + 4a 2 m 2 = 0

⇒ – 4c 2 + 4a 2 + 4a 2 m 2 = 0

⇒ 4c 2 = 4a 2 + 4a 2 m 2

⇒ c 2 = a 2 + a 2 m 2

⇒ c 2 = a 2 (1 + m 2)

Step-by-step explanation:

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