Question

the product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³)=0 is​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

ax²+bx+c=0

let the two roots be alpha and beta

we know that alpha+beta=-b/a

and alpha×beta=c/a

therefore alpha+beta=-[-(a+b)²]/(a²-b²)

=(a+b)²/(a+b)(a-b)

=a+b/a-b

and alpha×beta=a³-b³/(a²-b²)

since a³-b³=(a-b)(a²+ab+b²)

therefore alpha×beta=(a-b)(a²+ab+b²)/(a+b)(a-b)

=(a²+ab+b²)/a+b