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2 years ago

10

The sum of the squares of two positive numbers is 41 and the difference of the two squares of the numbers is 9. Find the numbers

. If there is more than one pair, use the "or" button.

1 answer:

vekshin12 years ago

8 0

Answer:

Step-by-step explanation:

41

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2 years ago

Which expression is equivalent to StartFraction 2 a + 1 Over 10 a minus 5 Endfraction divided by StartFraction 10 a Over 4 a squ

const2013 [10]

Answer:

$\frac{(2a + 1)^2}{50a}$

Step-by-step explanation:

Given

$\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1}$

Required

Find the equivalent

We start by changing the / to *

$\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1}$

$\frac{2a + 1}{10a - 5} * \frac{4a^2 - 1}{10a}$

Factorize 10a - 5

$\frac{2a + 1}{5(2a - 1)} * \frac{4a^2 - 1}{10a}$

Expand 4a² - 1

$\frac{2a + 1}{5(2a - 1)} * \frac{(2a)^2 - 1}{10a}$

$\frac{2a + 1}{5(2a - 1)} * \frac{(2a)^2 - 1^2}{10a}$

Express (2a)² - 1² as a difference of two squares

Difference of two squares is such that: $a^2- b^2= (a+b)(a-b)$

The expression becomes

$\frac{2a + 1}{5(2a - 1)} * \frac{(2a - 1)(2a + 1)}{10a}$

Combine both fractions to form a single fraction

$\frac{(2a + 1)(2a - 1)(2a + 1)}{5(2a - 1)10a}$

Divide the numerator and denominator by 2a - 1

$\frac{(2a + 1)((2a + 1)}{5*10a}$

Simplify the numerator

$\frac{(2a + 1)^2}{5*10a}$

$\frac{(2a + 1)^2}{50a}$

Hence,

$\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1}$ = $\frac{(2a + 1)^2}{50a}$

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