Cube root + quadratic equation - practice problems
Number of problems found: 9
- Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Equation 46771
Insert three numbers between the roots of the equation 4x² - 17x + 4 = 0 so that they form with the given GP numbers - Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube.
- 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. - Block-shaped 7976
A block-shaped pool with a volume of 200m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material. - Four-thirds 3852
Anton said: I have a natural number x. I'll get three times as much if I increase it to four-thirds. What number did Anton mean?
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