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tangare [24]
2 years ago
15

If x2+1/x2=18, find the value of x3−1/x3

Mathematics
2 answers:
Elden [556K]2 years ago
7 0

Answer:

There are 2 answers : 76 or -76

Step-by-step explanation:

x^2+\dfrac{1}{x^2} =18\\\\(x-\dfrac{1}{x} )^2=x^2+\dfrac{1}{x^2} -2=18-2=16\\\\x-\dfrac{1}{x}=4\ or\ x-\dfrac{1}{x}-4\\\\(x-\dfrac{1}{x} )^3=x^3-\dfrac{1}{x^3} -3x^2*\dfrac{1}{x}+3x*\dfrac{1}{x^2}\\\\=x^3-\dfrac{1}{x^3}-3(x-\dfrac{1}{x})\\\\x^3-\dfrac{1}{x^3}=(x-\dfrac{1}{x} )^3+3(x-\dfrac{1}{x})\\\\if\ x-\dfrac{1}{x}=4\ then \ x^3-\dfrac{1}{x^3}=4^3+3*4=64-12=76\\\\if\ x-\dfrac{1}{x}=-4\ then \ x^3-\dfrac{1}{x^3}=(-4)^3+3*(-4)=-64-12=-76\\\\

makvit [3.9K]2 years ago
7 0

Please find attached photograph for your answer.

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Step-by-step explanation:

As the absolute value equation is given:                                      

                                            | n−3 | = 5

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                  <em> So, n = 8 or n = −2</em> <em>is the correction solution.</em>

<em>Keywords: absolute value equation</em>

<em>Learn more about absolute value equation from brainly.com/question/680309</em>

<em>#learnwithBrainly</em>

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