Question

( a x^{2}+b x+c=0 )
( b x^{2}+c a+a=0 )
condition for a common root is
[
left(c a-a^{2}right)^{2}=left(a b-b^{2}right)left(b a-c^{2}right)
]
( c^{2} a^{2}+a^{4}-2 c a^{3}=a^{2} b^{2}-a b c^{2}-b^{3} a+b^{2} c^{2} )
( c^{2} a^{2}+a^{4}+a b c^{2}+b^{3} a=a^{2} b^{2}+b^{2} c^{2}+2 c a^{3} )
( aleft(a c^{2}+a^{3}+a b c^{2}+b^{3}right)= )

# - U Clu F-3. If ax + bx + C = 0 and bx2 + 2x + a = 0 have a common root and a, b, c are non-zero real numbers, then a3 + b3 + c3 find the value of abc

Solution