Answers: 3
![x^3+\left(\dfrac{1}{x}\right)^3=110\iff \left(x+\dfrac{1}{x}\right)^3-3\left(x+\dfrac{1}{x}\right)=110\\\\subtitute\ t=x+\dfrac{1}{x}\\\\t^3-3t=110\ \ \ \ |subtract\ 110\ from\ both\ sides\\\\t^3-3t-110=0\\\\t^3-25t+22t-110=0\\\\t(t^2-25)+22(t-5)=0\ \ \ |use\ a^2-b^2=(a-b)(a+b)\\\\t(t-5)(t+5)+22(t-5)=0\\\\(t-5)[t(t+5)+22]=0\iff t-5=0\ or\ \underbrace{t^2+5t+22=0}_{no\ solution}\\\\t=5\iff x+\dfrac{1}{x}=5\\\\\boxed{x+\dfrac{1}{x}=5}](/tpl/images/0416/9884/25925.png)
Another question on Mathematics
Mathematics, 21.06.2019 15:10
5.(04.07) two different plants grow each year at different rates, which are represented by the functions f(x) = 4* and g(x) = 5x + 2. what is the first year the f(x) height is greater than the g(x) height? year 3 year 0 year 2 year 1
Answers: 1
Mathematics, 21.06.2019 18:10
Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial
Answers: 1
Mathematics, 21.06.2019 20:00
True or false: the graph of y=f(bx) is a horizontal compression of the graph y=f(x) if b< 1
Answers: 2
You know the right answer?
If x^3 + 1/x^3 = 110 then find x + 1/x...
Questions
English, 18.06.2020 13:57
English, 18.06.2020 13:57
Mathematics, 18.06.2020 13:57
English, 18.06.2020 13:57
Mathematics, 18.06.2020 13:57
Chemistry, 18.06.2020 13:57
Biology, 18.06.2020 13:57
