(c²-ab)x²-2(a²-bc)x+b²-ac=0
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0
ANSWER
(c
2
=ab)x
2
−2(a
2
−bc)x+(b
2
−ac)=0
comparing with Ax
2
+Bx+C=0, we get
∴A=(c
2
−ab),B=−2(a
2
−bc),C=(b
2
−ac)
Roots of the quadratic eqn. are equal
⇒D=0
⇒
B
2
−4AC
=0
⇒B
2
−4AC=0
⇒B
2
=4AC
⇒[−2(a
2
−bc)
2
]=4(c
2
−ab)(b
2
−ac)
⇒4(a
2
−bc)
2
=4(c
2
−ab)(b
2
−ac)
⇒a
4
+b
2
c
2
−2a
2
bc=b
2
c
2
−ac
3
−ab
3
+a
2
bc
⇒a
4
+ab
3
+ac
3
=3a
2
bc.
⇒a(a
3
+b
3
+c
3
−3abc)=0.
∴a=oora
3
+b
3
+c
3
=3abc.
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