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2 years ago

Find the least common multiple of the pair of polynomials.2y^2 - 50 & y - 5

Mathematics

1 answer:

ZanzabumX [31]2 years ago

6 0

Answer:

The least common multiple is 2y^2 - 50.

Step-by-step explanation:

Least common multiple means the lowest thing you can multiply them both to. For example, the LCM of 2 and 4 is 2, because 2*2 = 4 and 4*1 = 4.

First, factor 2y^2 - 50.

2 (y^2 - 25)

2 (y - 5)(y + 5)

Looks like if we wanted to get 2y^2 - 50 starting with y - 5, we'd have to multiply it by 2(y + 5).

2y^2 - 50 * 1 = 2y^2 - 50

y - 5 * 2(y + 5) = 2y^2 - 50

<u>So their least common multiple is 2y^2 - 50.</u>

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Please help mee pleaseee

nalin [4]

Answer:

The exact answer in terms of radicals is $x = 5*\sqrt[3]{25}$

The approximate answer is $x \approx 14.62009$ (accurate to 5 decimal places)

===============================================

Work Shown:

Let $y = \sqrt[5]{x^3}$

So the equation reduces to -7 = 8-3y

Let's solve for y

-7 = 8-3y

8-3y = -7

-3y = -7-8 ... subtract 8 from both sides

-3y = -15

y = -15/(-3) ... divide both sides by -3

y = 5

-----------

Since $y = \sqrt[5]{x^3}$ and y = 5, this means we can equate the two expressions and solve for x

$y = 5$

$\sqrt[5]{x^3} = 5$

$x^3 = 5^5$ Raise both sides to the 5th power

$x^3 = 3125$

$x = \sqrt[3]{3125}$ Apply cube root to both sides

$x = \sqrt[3]{125*25}$

$x = \sqrt[3]{125}*\sqrt[3]{25}$

$x = \sqrt[3]{5^3}*\sqrt[3]{25}$

$x = 5*\sqrt[3]{25}$

$x \approx 14.62009$

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Find the least common multiple of the pair of polynomials.2y^2 - 50 & y - 5​

Find the least common multiple of the pair of polynomials.2y^2 - 50 & y - 5