Bikvadratic equation - math problemsThe 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.
Number of problems found: 18
- Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
By introducing a new variable solve biquadratic equation: ?
- Substitution method
Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
- Sequences AP + GP
The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.
- Geometric progressiob
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?
- Three members GP
The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
- Land boundary
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?
- Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
- Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
- Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm2 and volume V = 192 cm cubic. Calculate its radius and height.
- The cylinder
In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm2 and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
- Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2
- Two chords
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.
- Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
- MO Z8-I-1 2018
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.
- Eq2 2
Solve following equation with quadratic members and rational function: (x2+1)/(x-4) + (x2-1)/(x+3) = 23
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm2 greater than the upper base's content. Calculate the area of the upper base.
See also more information on Wikipedia.