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2 years ago

Divide. (4x^4 - 4x^2 - x-3) = (2x^2 – 3)

Mathematics

1 answer:

vekshin12 years ago

5 0

Answer:

$\frac{4x^4 - 4x^2 - x - 3}{2x^2 - 3}$

Step-by-step explanation:

Simplify: $\frac{4x^4 - 4x^2 - x - 3}{2x^2 - 3}$

<em>Checking for a perfect cube:</em>

4x⁴ - 4x² - x - 3 is not a perfect cube.

<em>Trying to factor by pulling out:</em>

Factoring: 4x⁴ - 4x² - x - 3
Thoughtfully split the expression at hand into groups, each group having two terms:
Group 1: - x - 3
Group 2: 4x⁴ - 4x³
Pull out from each group separately:
Group 1: (x + 3) • (-1)
Group 2: (x² - 1) • (4x²)
Bad news!! Factoring by pulling out fails:
The groups have no common factor and can not be added up to form a multiplication

<em>Final result:</em>

<em /> $\frac{4x^4 - 4x^2 - x - 3}{2x^2 - 3}$

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3 years ago

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3 years ago

7+3√5/3+√5 - 7-3√5/3-√5 = a + b√5

daser333 [38]

<h3>Given:-</h3>

$\\ \sf \implies\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } = a + \sqrt{5} b \\$

The value of a and b

<h3>Solution:-</h3>

$\\ \sf \implies\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } = a + \sqrt{5} b \\$

$\\ \sf \implies\frac{( \: 7 + 3 \sqrt{5} \: \: ( 3 - \sqrt{5}) \: \: - 7 - 3 \sqrt{5} \: \: ( 3 + \sqrt{5}) \: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{( \: 21 - 7 \sqrt{5} \: + 9 \sqrt{5} - 15) \: \: - ( \: 21 + 7 \sqrt{5} \: - 9 \sqrt{5} + 15)\: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{( \: 6 + 2 \sqrt{5} ) \: \: - ( \: 6 - 2 \sqrt{5} )\: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 6 + 2 \sqrt{5} \: \: - \: \: 6 - 2 \sqrt{5} \: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 4 \sqrt{5} \: \: }{3 {}^{2} - {\sqrt{5} }^{2} } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 4 \sqrt{5} \: \: }{ \: \: \: \: 9 - 5 \: \: \: } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 4 \sqrt{5} \: \: }{ \: \: \: \: 4 \: \: \: } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: \cancel{4 } \sqrt{5} \: \: }{ \: \: \: \: \cancel{4 }\: \: \: } = a + \sqrt{5} \: b\\$

$\\ \sf \implies \: \sqrt{5} = a + \sqrt{5} \: b\\$

we can also write it as ;

$\\ \sf \implies \: 0 + \sqrt{5} = a + \sqrt{5} \: b\\$

★<u> </u><u>Henceforth, the value of a and b are</u> :

→ a = 0

→ b = 1

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2 years ago

Read 2 more answers

Divide. (4x^4 - 4x^2 - x-3) = (2x^2 – 3)​

Divide. (4x^4 - 4x^2 - x-3) = (2x^2 – 3)