Question

x²+1/x²=17/4 then find -1/x,x³-1/x³​

Answer 1

Answer:Well, I always use the following fact to find roots of the polynomial:

Fact: If s|t is a root of polynomial a(x)=a0+a1x+a2x2+….+anxn , then s|a0 and t|an .

Thus for a(x)=x3+x2+x−155=0 , s={1,5,31,155} and t={1} . Thus, if it has a rational solution, then it must be one of those: −1,−5,−31,−155,1,5,31,155 . You can try all of them and check that 5 is one of the solution because a(5)=125+25+5–155=0 .

Now, since we find one of the solution, we can find the quadratic equation by dividing a(x) over (x−5) . So, we get: x2+6x+31 . Now, if you use quadratic formula, we get two complex numbers, i.e. x1=−3+i22−−√ and x2=−3−i22−−√ .

So, the solution of a(x)=x3+x2+x−155 is 5,−3+i22−−√ and −3−i22−−√ .

Step-by-step explanation: