If x,,,, are the roots of
the quadcratic equation cx'+bx
ax+6
and cto find the value of
Caxi + b)^2 + (axy + b) 2 in tcoins
of a, b, c.
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Answer:
ANSWER
Let α,β,γ be the roots of ax
3
+bx
2
+cx+d=0
α+β+γ=
a
−b
αβ+βγ+γα=
a
c
αβγ=
a
−d
As α,β,γ are in H.P
β=
αβ+βγ+γα
3αβγ
⇒β=
c
−3d
Substituting this in equation we get
a(
c
−3d
)
3
+b(
c
−3d
)
2
+c(
c
−3d
)+d=0
⇒2c
3
+27ad
2
=9bcd
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