- #1
Sawarnik
- 7
- 0
600*sqrt{1-a^2/400}=578-a^2/2
Shorter and elegant tricks would be welcome!
Shorter and elegant tricks would be welcome!
Evgeny.Makarov said:The straigtforward way is to denote $a^2$ by $x$ and take the square of both sides. Then both sides become quadratic polynomials. After finding $x$, it is necessary to check that $x\le 400$ to avoid gaining extra roots during squaring. The left-hand side can be simplified to $30\sqrt{400-a^2}$; then both sides can be multiplied by 2 to avoid fractions. It may help a little to denote $400-x$ by $y$.
A quadratic equation is an equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
The most common method for solving a quadratic equation is by factoring. First, rearrange the equation so that it is in the form of (ax + b)(cx + d) = 0. Then, set each factor equal to 0 and solve for x. If factoring is not possible, you can also use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
You can check your solution by substituting the value of x into the original equation and seeing if it equals 0. If it does, then your solution is correct.
Solving a quadratic equation with paper and pen allows for a more thorough understanding of the problem and the steps involved in finding a solution. It also allows for a more organized and clear presentation of the solution.
While there may be some shortcuts or tricks for solving certain types of quadratic equations, it is important to understand the underlying concepts and methods for solving quadratic equations. This will allow for a better understanding and ability to solve a variety of quadratic equations.