+958 Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$
+49 (a+b)2=a2+b2+2ab=6+2ab=16, so ab=5. If we do (a+b)3, we can expand it to a3+a2b+ab2+b3 via the binomial theorem. If we focus on the middle terms, we notice we can turn it into ab(a+b), which is equal to 5*4=20. Therefore, a3+b3=64−20=44.
Feel free to tell me if I did anything wrong! :D
+49 (a+b)2=a2+b2+2ab=6+2ab=16, so ab=5. If we do (a+b)3, we can expand it to a3+a2b+ab2+b3 via the binomial theorem. If we focus on the middle terms, we notice we can turn it into ab(a+b), which is equal to 5*4=20. Therefore, a3+b3=64−20=44.
Feel free to tell me if I did anything wrong! :D
