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If the equation (
Answers
Step-by-step explanation:
(a+b).is the answer of your question
Answer:
Given:
The roots of the equation (a2 + b2)x2 -2b(a+c)x+(b2 +c2) = 0 are equal
To find:
If the roots of the eqn (a2 + b2)x2 -2b(a+c)x+(b2 +c2) = 0 are equal, then
Solution:
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
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Therefore, option B) b² = ac is correct option.