Mathematics: Apositive integer is 4 more than 12 times another. their product is 5896. find the two integers

Apositive integer is 4 more than 12 times another.

Ответ:

dctjr

06.01.2022

X=12y+4
xy=5896
x=5896/y

5896/y=12y+4
5896=12y^2+4y
12y^2+4y-5896=0
solving quadratic equation
y=22
y=-22.33
negative is not possible so y=22
then x=268

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Ответ:

izzyp619

28.08.2021

Mathematics

Differentiate implicitly:
3x^2-y-xy'+3y^2y'=0

Solve for y
$y'(3y^2-x)=y-3x^2
\\
\\y'={y-3x^2\over3y^2-x}$

When the tangent is parallel to the x-axis we have y'=0, so we must solve
$y'={y-3x^2\over3y^2-x}=0\implies y=3x^2$

To find the actual value of x we plug this expression for y into the original equation
$x^3-3x^3+27x^6=0
\\
\\x^3(27x^3-2)=0\implies x=\{0,{\sqrt[3]2\over3}\}$

Plugging this into the formula for y above gives the points
$(0,0)\text{ and }({\sqrt[3]2\over3},{\sqrt[3]4\over3})$

which is where our tangent will be parallel to the x-axis.

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Apositive integer is 4 more than 12 times another. their product is 5896. find the two integers

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