Evaluation of expressions

If a2-3a+1=0, find

(i)a2+1/a2
(ii) a3+1/a3

Correct result:

x1 =  7
x2 =  7
y1 =  18
y2 =  18

Solution:

a2−3a+1=0  a2−3a+1=0 a2−3a+1=0  p=1;q=−3;r=1 D=q2−4pr=32−4⋅1⋅1=5 D>0  a1,2=−q±D2p=3±52 a1,2=1.5±1.1180339887499 a1=2.6180339887499 a2=0.38196601125011   Factored form of the equation:  (a−2.6180339887499)(a−0.38196601125011)=0 x1=a12+1/a12=2.6182+1/2.6182=7

Our quadratic equation calculator calculates it.

x2=a22+1/a22=0.3822+1/0.3822=7x_{2}=a_{2}^2+1/a_{2}^2=0.382^2+1/0.382^2=7
y1=a13+1/a13=2.6183+1/2.6183=18y_{1}=a_{1}^3+1/a_{1}^3=2.618^3+1/2.618^3=18
y2=a23+1/a23=0.3823+1/0.3823=18y_{2}=a_{2}^3+1/a_{2}^3=0.382^3+1/0.382^3=18

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