If a+b=9 then find the value of a^3 +27ab+b^3
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Step-by-step explanation:
a>b>0
a
3
+b
3
+27ab=729
⇒a
3
+b
3
+(−9)
3
−3ab(−9)=0
Using:- a
3
+b
3
+c
3
−3abc=(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
⇒(a+b−9)(a
2
+b
2
−ab+9a+9b+81)=0
therefore
a+b−9=0
a+b=9
f(x)=ax
2
+bx−9=0 →α+β=
a
−b
⇒αβ=
a
−9
(α<β)
a>b>0
f(1)=a+b−9
either α=1 or β=1
if β=1
α=
a
−9
We need
4β−aα=4×1−ax(−
a
9
)
=4+9=13.
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