Expression with powers

If x-1/x=5, find the value of x4+1/x4


v =  727


x1/x=5  x25x1=0  a=1;b=5;c=1 D=b24ac=5241(1)=29 D>0  x1,2=b±D2a=5±292 x1,2=2.5±2.6925824035673 x1=5.1925824035673 x2=0.19258240356725   Factored form of the equation:  (x5.1925824035673)(x+0.19258240356725)=0  v1=x14+1/x14=5.19264+1/5.19264=727 v2=x24+1/x24=(0.1926)4+1/(0.1926)4=727  v1=v2 v=v1=727x-1/x=5 \ \\ \ \\ x^2 -5x -1=0 \ \\ \ \\ a=1; b=-5; c=-1 \ \\ D=b^2 - 4ac=5^2 - 4\cdot 1 \cdot (-1)=29 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 5 \pm \sqrt{ 29 } }{ 2 } \ \\ x_{1,2}=2.5 \pm 2.6925824035673 \ \\ x_{1}=5.1925824035673 \ \\ x_{2}=-0.19258240356725 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -5.1925824035673) (x +0.19258240356725)=0 \ \\ \ \\ v_{1}=x_{1}^4+1/x_{1}^4=5.1926^4+1/5.1926^4=727 \ \\ v_{2}=x_{2}^4+1/x_{2}^4=(-0.1926)^4+1/(-0.1926)^4=727 \ \\ \ \\ v_{1}=v_{2} \ \\ v=v_{1}=727

Checkout calculation with our calculator of quadratic equations.

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!

Tips to related online calculators

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. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  4. Expressions 3
    parabola2_1 If k(x+6)= 4x2 + 20, what is k(10)=?
  5. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  6. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  7. Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8
  8. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  9. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  10. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  11. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  12. Product
    floring The product of two consecutive odd numbers is 8463. What are this numbers?
  13. 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
  14. Quadratic equation
    parabola_1 Solve quadratic equation: 2x2-58x+396=0
  15. Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  16. 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?
  17. Line
    skew_lines It is true that the lines that do not intersect are parallel?