If $a^3 + b^3 = 20$ and a + b = 5, then find the value of $a^4+b^4$.
Answer & explanation
Correct answer: option 4
a + b = 5
a3 + b3 = 20
(a + b)3 = a3 + b3 + 3ab(a + b)
(a + b)3 = a3 + b3 + 3ab(a + b)
53 = a3 + b3 + 3ab(5)
= 3ab(5) = 125 – 20
= ab = 7
Now,
(a + b)2 = a2 + b2 + 2ab
= 52 = a2 + b2 + 2 × 7
= a2 + b2 = 25 – 14 = 11
We know that, (a2 + b2)2 = a4 + b4 + 2a2b2
112 = a4 + b4 + 2 × 49
= a4 + b4 = 121 – 98 = 23