Biquadratic equation - practice problems
The fourth-order equation in the form ax4 + bx2 + c = 0 is a biquadratic equation. It is solved by substitution t = x2, 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.Instructions: Take your time with each problem and write out how you solved it step by step.
Number of problems found: 29
- Sum of squares
If the first number is 80% of the second number and 4 times the sum of their squares is 656, find the numbers. - Three numbers
The product of three natural numbers is 600. If we reduced one factor by 10, the product would decrease by 400. If we increased one factor by 5 instead, the product would increase to twice the original value. Which three numbers have this property? - Unknown number quarter
A quarter of an unknown number multiplied by 4 equals 30% of that unknown number. Determine the unknown number. - Combinations - elements
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? - Members
A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has an 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, the second 4, and keep the third, we get the geometric series. 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 is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - Faces diagonals
Find the cuboid volume if the cuboid's diagonals are x, y, and z (wall diagonals or three faces). Solve for x=1.6, y=1.8, z=1.6 - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - Geometric progressiob
If the sum of four consecutive terms of a geometric progression is 80 and the arithmetic mean of the second and fourth terms 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 the 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] - Cone Volume Surface Height
In the rotating cone = 100π S rotating cone = 90π v =? r =?
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