If a + b = 6,
\(\frac{2}{5}\)ab = 4, then
find the value of a3 + b3.
Answer & explanation
Correct answer: option 4
\(\frac{2}{5}\)ab = 4
ab = 10
Now,
⇒ (a+b)2 = (6)2
⇒ a2 + b2 + 2ab = 36
⇒ a2 + b2 = 36 - 2\(\times\) 10 = 16
Therefore,
a3 + b3 = (a+b) (a2 + b2 - ab)
= 6 ( 16 -10) = 36