Biquadratic equation - practice 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: 26
- Combinations 70714
If we increase the number of elements by 1, the number of combinations of the third class without repetitions increases by 10. How many elements do we have?
- Right triangle generator
Detective Harry Thomson found on the Internet a generator of the lengths of the sides of right triangles according to which he must apply: a = 2xy, b = x² - y², c = x² + y², where are natural numbers and x & gt; y. Is it a working generator?
A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has even index) has a value of 42. Find these members.
- Given 2
Given g(x)=x2+x+1 where x=t². What is g(t²)?
- Polynomial roots
Find the other zeroes of the polynomial 2x4+3x³-3x²-6x-2, if two of them are root2 & -root2
- 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 area. Calculate the area of the upper base.
- 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.
- 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.
- Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
- 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?
- 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 the circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
- Geometric progressiob
If the sum of four consecutive terms of a geometric progression is 80 and the arithmetic mean of the 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.
- Eq2 2
Solve following equation with quadratic members and rational function: (x2+1)/(x-4) + (x2-1)/(x+3) = 23
- Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
- Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =?
- Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and side is 13 cm long.
- Substitution method
Solve goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2
- Diagonals of the rhombus
How long are the diagonals e, f in the diamond if its side is 5 cm long and its area is 20 cm²?
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