2 years ago

What does a rational number plus an irrational number equal?

Mathematics

1 answer:

galben [10]2 years ago

3 0

The sum must be irrational in contradiction to it being rational

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Identify all of the following solutions of square root of x plus 14 end root plus 2 equals x.

BabaBlast [244]

$\bf \sqrt{x+14}+2=x\implies \sqrt{x+14}=x-2\impliedby \textit{squaring both sides}
\\\\\\
(\sqrt{x+14})^2=(x-2)^2\implies x+14=x^2-4x+4
\\\\\\
0=x^2-5x-10\impliedby \textit{now, using the quadratic formula}
\\\\\\
x=\cfrac{5\pm\sqrt{(-5)^2-4(1)(-10)}}{2(1)}\implies x=\cfrac{5\pm\sqrt{25+40}}{2}
\\\\\\
x=\cfrac{5\pm \sqrt{65}}{2}\implies x=
\begin{cases}
\cfrac{5+ \sqrt{65}}{2}\\\\
\cfrac{5- \sqrt{65}}{2}
\end{cases}$

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2 years ago

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Nutka1998 [239]

3/5 miles = 4 miles
1/5 miles = 4/3 miles
5/5 (1) mile = 20/3 miles = 6 2/3 miles
6 2/3 miles per hour

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2 years ago

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Lady bird [3.3K]

Answer:

A.Linear

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I need to show how to find these solutions 1/4 and 3/4 by completing the square!

Arlecino [84]

Answer:

See explanation, and ask for more details if unclear!

Step-by-step explanation:

The perfect square of this equation is $x^2-x+\frac{1}{4}$ , since the square would be $(x-\frac{1}{2})^2$ . 1/4=4/16, meaning that you can set up the equation in the following way: