# Evaluation of expressions

If a2-3a+1=0, find

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

Result

x1 =  7
x2 =  7
y1 =  18
y2 =  18

#### Solution:

$\ \\ a^2-3a+1=0 \ \\ a^2 -3a +1=0 \ \\ \ \\ p=1; q=-3; r=1 \ \\ D=q^2 - 4pr=3^2 - 4\cdot 1 \cdot 1=5 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 3 \pm \sqrt{ 5 } }{ 2 } \ \\ a_{1,2}=1.5 \pm 1.1180339887499 \ \\ a_{1}=2.6180339887499 \ \\ a_{2}=0.38196601125011 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -2.6180339887499) (a -0.38196601125011)=0 \ \\ x_{1}=a_{1}^2+1/a_{1}^2=2.618^2+1/2.618^2=7$

Checkout calculation with our calculator of quadratic equations.

$x_{2}=a_{2}^2+1/a_{2}^2=0.382^2+1/0.382^2=7$
$y_{1}=a_{1}^3+1/a_{1}^3=2.618^3+1/2.618^3=18$
$y_{2}=a_{2}^3+1/a_{2}^3=0.382^3+1/0.382^3=18$

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