perplexus.info :: Just Math : Power after power

Power after power (Posted on 2023-03-22)

If
a+b=1
&
a^2+b^2=2

How much is a^11+b^11?

No Solution Yet Submitted by Ady TZIDON

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How to solve without really thinking...

Comment 3 of 3 |

... but you do get to practice the finer tools of Matlab.

syms a b

eqs=[a+b==1,a^2+b^2==2]

s=solve(eqs);

a=s.a

b=s.b

simplify(a(1)^11+b(1)^11)

simplify(a(2)^11+b(2)^11)

finds

a =

3^(1/2)/2 + 1/2

1/2 - 3^(1/2)/2

b =

1/2 - 3^(1/2)/2

3^(1/2)/2 + 1/2

ans =

989/32

ans =

989/32

indicating a and b are

1/2 + sqrt(3)/2 and 1/2 - sqrt(3)/2

in either order.

and a^11 + b^11 = 989/32

Posted by Charlie on 2023-03-22 13:22:57

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