Asked by Noor
Find the values of a^2 + b^2 and a^4 + b^4 when a + b =5 and Ab = 4
Answers
Answered by
Reiny
recall that
(a+b)^2 = a^2 + b^2 + 2ab
so
5^2 = a^2 + b^2 + 2(4)
a^2 + b^2 = 25-8 =17
similarly
(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
5^4 = (a^4 + b^4) +4ab(a^2 + b2) + 6(ab)^2
625 = (a^4 + b^4) + 4(4)(17) + 6(4^2)
take over
(a+b)^2 = a^2 + b^2 + 2ab
so
5^2 = a^2 + b^2 + 2(4)
a^2 + b^2 = 25-8 =17
similarly
(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
5^4 = (a^4 + b^4) +4ab(a^2 + b2) + 6(ab)^2
625 = (a^4 + b^4) + 4(4)(17) + 6(4^2)
take over
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.