if a+b>k√ab;a,b belongs to R+ then k=
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Answer:
Since the given equation has imaginary roots
⇒D<0⇒(a+b+c)
2
−4(ab+bc+ca)<0
⇒(a
2
+b
2
+c
2
−2ab−2bc+2ac)<4ac
⇒(−a+b−c)
2
<4ac ⇒−2
ac
<a−b+c
⇒(a+c+2
ac
)>b ⇒(
a
+
c
)
2
>b⇒
a
+
c
>
b
.
Similarly,
b
+
c
>
a
and
a
+
b
>
c
.
Therefore,
a
,
b
,
c
can be the sides of a triangle.
Step-by-step explanation:
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