Question

if the roots of the equation
(a²+b²)x²-2b(a+c)x+c²+b²=0
are equal,then​

Answer 1

Answer:

From given, we have.

The roots of the eqn (a2 + b2)x2 -2b(a+c)x+(b2 +c2) = 0 are equal

The condition for the roots of a quadratic equation to be equal is,

b² - 4ac = 0

\begin{gathered}\left(-2b\left(a+c\right)\right)^2-4\left(\left(a^2+b^2\right)\left(b^2+c^2\right)\right)=0\\\\-4b^4+8ab^2c-4a^2c^2=0\end{gathered}

(−2b(a+c))

2

−4((a

2

+b

2

)(b

2

+c

2

))=0

−4b

4

+8ab

2

c−4a

2

c

2

=0

\begin{gathered}-4c^2a^2+8b^2ca-4b^4=0\\\\\left(8b^2c\right)^2-4\left(-4c^2\right)\left(-4b^4\right)=0\\\\a=\dfrac{-8b^2c}{2\left(-4c^2\right)}\end{gathered}

−4c

2

a

2

+8b

2

ca−4b

4

=0

(8b

2

c)

2

−4(−4c

2

)(−4b

4

)=0

a=

2(−4c

2

)

−8b

2

c

upon simplifying, we get,

-8ac² = -8b²c

ac² = b²c

ac = b²