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.

Another totally different approach is tho solve for $a$ and $b$ using :
$$ab = 2, \qquad a+b = 5$$
This is like solving a second order polynomial $(x+a)(x+b) = x^2 + (a+b)x+ab$ where the roots are $-a$ and $-b$.
So you could solve the polynomial $x^2 + 5x + 2 = 0$, deduce $a$ and $b$ and calculate $a^4+b^4$.  
