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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.
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:
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.
For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1.
For this derivation, we want to simplify the expression (). To do this, we begin with the simpler expression log b ( x ) {\displaystyle \log _{b}(x)} . Since we will be using log b ( x ) {\displaystyle \log _{b}(x)} often, we will define it as a new variable: Let m = log b ( x ) {\displaystyle m=\log _{b}(x)} .
The Honda 0 SUV, right, and Honda 0 Saloon EV prototypes are on display at the Honda booth during the CES tech show Tuesday, Jan. 7, 2025, in Las Vegas.
The company said it's considering incorporating AI technology from Amazon Web Services to help individuals find nearby charging facilities, for example, or simplify payments.
This sweater and wide-leg pant set looks way more high-end than the price suggests. The slouchy oversized silhouette is the perfect comfy, ready-for-a-cozy-day-at-home fit.