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The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
Now 2b 2 and a 2 cannot be equal, since the first has an odd number of factors 2 whereas the second has an even number of factors 2. Thus | 2 b 2 − a 2 | ≥ 1 . Multiplying the absolute difference | √ 2 − a / b | by b 2 ( √ 2 + a / b ) in the numerator and denominator, we get [ 17 ]
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
This drove overall Q3 revenue to hit a record $35.1 billion, up 94% over the previous year. Nvidia's financial might Nvidia's massive revenue growth leads into the other factor making it a top AI ...
Simplifying this further gives us the solution x = −3. It is easily checked that none of the zeros of x ( x + 1)( x + 2) – namely x = 0 , x = −1 , and x = −2 – is a solution of the final equation, so no spurious solutions were introduced.
Here are the 10 most traded cryptocurrencies in the past 30 days with a market cap of at least $1 billion. Data as of Oct. 25, 2024, from CoinMarketCap.com. Cryptocurrency.
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.