Thejus15idn
Answered

Find detailed and accurate answers to your questions on IDNLearn.com. Discover comprehensive answers to your questions from our community of knowledgeable experts.

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

Sagot :

Caylusidn

Answer:

There are 2 answers : 76 or -76

Step-by-step explanation:

[tex]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\\\\[/tex]

Please find attached photograph for your answer.

View image Аноним
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.