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:

a23a+1=0  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

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



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
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?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Expressions 3
    parabola2_1 If k(x+6)= 4x2 + 20, what is k(10)=?
  • Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  • Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  • Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  • Find the 2
    square_4 Find the term independent of x in the expansion of (4x3+1/2x)8
  • Hyperbola equation
    hyperbola_4 Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
  • Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  • Completing square
    eq2_5 Solve the quadratic equation: m2=4m+20 using completing the square method
  • Geometric seq
    eq222_1 Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
  • On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  • Equation of circle 2
    circle_axes Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
  • Substitution method
    500px-Sine_cosine_plot.svg Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
  • Solve equation
    hrusky_2 solve equation: ?
  • Expressions
    equation Expression (3a-7).(3a+7) is identical with: ?
  • Geometric progressiob
    eq2 If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
  • Non linear eqs
    q2_non_linear Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
  • Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160