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2 years ago

What is the best first step in solving the equation 3 +

" title="3\sqrt[6]{x}" alt="3\sqrt[6]{x}" align="absmiddle" class="latex-formula"> = 5?

Mathematics

1 answer:

Andreas93 [3]2 years ago

6 0

$3+3\sqrt[6]{x}~~ = ~~5\implies \stackrel{\textit{1st step,-3 to both sides}}{3\sqrt[6]{x}~~ = ~~2}\implies \sqrt[6]{x}=\cfrac{2}{3} \\\\\\ (\sqrt[6]{x})^6=\left( \cfrac{2}{3} \right)^6\implies x=\cfrac{2^6}{3^6}\implies x=\cfrac{64}{729}$

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Please help solve this system of equations

stepan [7]

Make a substitution:

$\begin{cases}u=2x+y\\v=2x-y\end{cases}$

Then the system becomes

$\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}$

Simplifying the equations gives

$\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}$

which is to say,

$\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}$

$\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81$

$\implies\dfrac uv=\pm27$

$\implies u=\pm27v$

Substituting this into the new system gives

$\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1$

$\implies u=\pm27$

Then

$\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13$

(meaning two solutions are (7, 13) and (-7, -13))

8 0

2 years ago

SUPER EASY PLEASE ANSWER BY 11 PM WILL GIVE BRAINLEIST PLS NO UNRELATED ANSWERS. The population of a small town is expected to d

Viktor [21]

Answer:

1504

Step-by-step explanation:

47*2^25/5

47*2^5

47*32=1504

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3 years ago

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PLEASE HELP THIS WAS DUE LAST WEEK!!!!!!!!!!!!!

GrogVix [38]

Answer:

Zack is correct

Step-by-step explanation:

when we plot out all the points we see that not all sides are the same length, which is techinally defines a square. Because of the different sides lengths we know it is a rhombus.

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3 years ago

The price of a video game is $35.60. if you purchase the video game for $30.26 with a coupon, what percent of the original price

prohojiy [21]

35.60-30.26=5.34. 5.34=13%

3 0

3 years ago

The sum of two trinomials is 7x2 - 5x + 4. If one of the trinomials is 3x2 + 2x - 1, then what is the other trinomial?

allsm [11]

Total=sum of parts
Total= trinomial 1 + trinomial 2
Also, total - trinomial 1=trinomial 2

7x² - 5x + 4 -(3x² + 2x - 1)=missing trinomial
7x²-5x+4+(-1 )(3x²+2x-1 ) distribution of -1
7x²-5x+4+(-1)(3x²)+(-1)(2x)-(-1)(1)
7x²-5x+4-3x²-2x+1 simplified
7x²-3x²-5x-2x+4+1 commutative
4x²-7x+5 SOLUTION

4 0

3 years ago

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