Question

If x^4 + 1/x^4 = 47

x^3 + 1/x^3=?​

Answer 1

x4+1x4=47(1)

(x2+1x2)2=x4+1x4+2

(x2+1x2)2=47+2=49

(x2+1x2)=49−−√=±7

∵(x2+1x2)>0∀x∈R

(x2+1x2)2=7(2)

(x+1x)2=x2+1x2+2

(x+1x)2=7+2=9

(x+1x)=±3(3)

(x+1x)2(x+1x)=(x3+1x3)+(x+1x)

⟹

7×(±3)=(x3+1x3)(±3)

(x3+1x3)=±18