Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solutions are
and
.
Solución
We start with the system
Step 1. Express
in terms of
from the first equation:
Step 2. Substitute
into the second equation:
Step 3. Expand the square and simplify:
Subtract
from both sides:
Divide the entire equation by
to simplify:
Step 4. Solve the quadratic equation
using the quadratic formula:
where
,
, and
. First, compute the discriminant:
Now, substitute into the formula:
Thus, the two solutions for
are:
Step 5. Find
using
.
For
:
For
:
Final Answer:
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
To solve the equations
and
, we can start with the first equation.
From
, we can express
in terms of
:
Now, we can substitute this expression for
into the second equation:
Expanding
:
Combining like terms gives us:
Subtracting 43 from both sides results in:
Now, we can simplify this quadratic equation by dividing all terms by 6:
Next, we can factor the quadratic:
Setting each factor to zero gives us the solutions:
Now we can substitute these values back into the expression for
.
For
:
For
:
Thus, the pairs
that solve the original equations are:

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