Answer:
Given equation is (1+m
2
)x
+2mcx+c
−a
=0
We need to prove c
=a
(1+m
)
The roots are real and equal Δ=0.
Therefore, b
−4ac=0
⇒(2mc)
−4(1+m
)(c
)=0
⇒4m
c
−4(c
+m
−m
a
⇒m
−(c
−c
+a
⇒c
m
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Answers & Comments
Answer:
Given equation is (1+m
2
)x
2
+2mcx+c
2
−a
2
=0
We need to prove c
2
=a
2
(1+m
2
)
The roots are real and equal Δ=0.
Therefore, b
2
−4ac=0
⇒(2mc)
2
−4(1+m
2
)(c
2
−a
2
)=0
⇒4m
2
c
2
−4(c
2
−a
2
+m
2
c
2
−m
2
a
2
)=0
⇒m
2
c
2
−(c
2
−a
2
+m
2
c
2
−m
2
a
2
)=0
⇒m
2
c
2
−c
2
+a
2
−m
2
c
2
+m
2
a
2
=0
⇒c
2
=a
2
+a
2
m
2
⇒c
2
=a
2
(1+m
2
)