- 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

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( 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)= )

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