Let a and b be real numbers such that a + b = 4 and a^4 + b^4 = 16.

(a) Find all possible values of ab

(b) Find all possible values of a + b

(c) Find all possible values of a and b

Guest Dec 2, 2022

#1**0 **

Attention Melody, please:

If you square a + b =4, you get this:

a^2 + b^2 + 2ab =16

Set ab=p and note that:

a^2 + b^2=2[8 - p]. Square again to get:

a^4 + 2a^2b^2 + b^4 =4[8 - p]^2

And therefore, the right-hand side:

=16 + 2p^2=4(p^2 -16p + 64). Simplify and re-order, you get:

P^2 - 32p + 120=0

p==16+or-sqrt(132)

Melody: I have reached this far! But, I'm stuck as how to get the values of a and b ?

Guest Dec 2, 2022