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:

 a23a+1=0 a23a+1=0  p=1;q=3;r=1 D=q24pr=32411=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:  (a2.6180339887499)(a0.38196601125011)=0 x1=a12+1/a12=2.6182+1/2.6182=7 \ \\ 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.

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



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  2. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  3. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  4. Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160
  5. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  6. Solve equation
    hrusky_2 solve equation: ?
  7. Reciprocal value
    fx How do I calculate a number x that is 9 greater than its reciprocal (1/x)?
  8. Difference AP 4
    sequence_geo_1 Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
  9. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  10. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  11. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  12. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  13. Quadratic inequation
    eq2_8 If 5x + x² > 100, then x is not
  14. Quadratic equation
    Parabola_tangent Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
  15. Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  16. The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?