<s>[INST] Working out the value of $a^4+b^4$ If $ab = 2$ and $a+b = 5$ then calculate the value of $a^4+b^4$
My approach:
$$a^4+b^4 = (a+b)^4-4a^3b-6a^2b^2-4ab^3$$
$$=(5)^4-6(ab)^2-4ab.a^2-4ab.b^2$$
$$=(5)^4-6(24)-4ab(a^2-b^2)$$
$$=(5)^4-6(24)-8(a+b)(a-b)$$
$$=(5)^4-6(24)-8(5)(a-b)$$
I am a little stuck now and any help will be appreciated.
 [/INST] An easier approach: Since $ab = 2$, then 
$$ (a+b)^2 = 25 $$.
Hence
$$ a^2 + b^2 + 2ab = 25 \iff a^2 + b^2 = 25 - 2 ab = 21 $$
Hence,
$$ (21)^2 = (a^2 + b^2)^2 = a^4 + b^4 + 2 a^2 b^2 = a^4 + b^4 + 2(2)^2 $$
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