Bikvadratic equation - math word problems

The fourth-order equation in the form ax^4 + bx^2 + c = 0 is a biquadratic equation. It is solved by substitution t = x^2, which converts the equation into a quadratic equation. It will give us one, two, or no roots. Subsequently, the substitution equation will be solved, which usually doubles the number of roots.

  1. Land boundary
    rt_triangle The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
  2. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
  3. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  4. 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?
  5. Three members GP
    exp_growth The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
  6. Eq2 2
    kardan3rd Solve following equation with quadratic members and rational function: (x2+1)/(x-4) + (x2-1)/(x+3) = 23
  7. 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]
  8. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  9. Substitution method
    500px-Sine_cosine_plot.svg Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
  10. MO Z8-I-1 2018
    age_6 Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
  11. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  12. Diamond diagonals
    kosostvorec Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
  13. Cuboid
    cuboid Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  14. Biquadratic
    bikvadraticka By introducing a new variable solve biquadratic equation: ?

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