If a+b=2 and a²+b²=3, what does a⁴+b⁴ equal ?

If a+b=2 and a²+b²=3, what does a⁴+b⁴ equal ? I got this in a test I need help pls
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1 Answer

a4+b4=(a+b)4-4a3b-6a2b2-4ab3=16-4ab(a2+b2)-6a2b2=16-12ab-6a2b2.

(a+b)2=4=a2+2ab+b2=3+2ab; 2ab=1, ab=½, a2b2=(ab)2=¼.

a4+b4=16-12/2-6/4=16-6-3/2=17/2.

by Top Rated User (1.1m points)

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