(x + 1/x) = 6 the value of ( x5 + 1/x5 ) = ?

• (x + 1/x) = 6
  x^2 + 1/x^2 = 34 , x^3 + 1/x^3 = 198 ,
  (x^2 + 1/x^2 ) (x^3 + 1/x^3 ) = 198*34
  x^5+ 1/x^5= 6726
• 8 years agoHelpfull: Yes(36) No(13)
• (x+1/x)^2=36=x^2+2*x*1/x+1/x^2 .so x^2+1/x^2=34. (x^2+1/x^2)*(x+1/x)=x^3+x+1/x1/x3.=x3+1/x^3=34*6-6=198. again. (x3+1/x^3)*(x+1/x)=x4+x^2+1/x^2+1/x^4. x^4+1/x^4=198*6-34=1154. (x4+1/x^4)*(x+1/x)= x5+x3+1/x^3+1/x^5. x5+1/x^5=1154*6-198=6726
• 8 years agoHelpfull: Yes(10) No(1)
• (x+1/x)=6
  (x+1/x)^2 = 36
  (x^2 +1/x^2) =34 [According to (a+b)^2]
  (x^3+1/x^3) = 198 [According to (a+b)^3]
  (x^3+1/x^3)(x^2+1/x^2) = 34*198
  (x^5+1/x^5)(x+1/x) = 6732
  (x^5 + 1/x^5)=6732-6=6726. [ Given: (x+1/x)=6]
• 6 years agoHelpfull: Yes(4) No(2)
• (x+1/x)=6
  (x+1/x)^2=36
  x sq + 1/x sq =34
  (x^3+1/x^3)=(x+1/x)^3- 3x*1/x(x+1/x)
  x cube +1/x cube =198
  (x cube +1/x cube)(x sq +1/ x sq)=x^5 + x + 1/ x 1/x^5
  =(x^5 +1/x^5) + (x+1/x)
  
  198*34= (x^5 +1/x^5) + (x+1/x)
  (198*34) /6= (x^5 +1/x^5)
  (x^5 +1/x^5) =1122
• 8 years agoHelpfull: Yes(2) No(18)
• (x+1/x)^2=36. (x+1/x)^5=6^5=7776. (x+1/x)^5=x^5+5x^3+10x+10/x+5/x^3+1/x^5. =(x^5+1/x^5)+5(x^3+1/x^3)+10(x+1/x). =(x5+1/x^5)+5(x+1/x)(x2-1+1/x^2)+10(x+1/x)=7776. (x5-1/x^5)=7776-5(6*33)+60=6726
• 8 years agoHelpfull: Yes(1) No(3)
• x+1x=3
  
  ⟹(x+1x)2=9
  
  ⟹x2+1x2+2=9
  
  ⟹x2+1x2=7
  
  Again,
  
  (x+1x)3=27
  
  ⟹x3+1x3+3(x+1x)=27
  
  ⟹x3+1x3=27−3×3=18
  
  Now,
  
  (x2+1x2)(x3+1x3)=(x5+1x5)+(x+1x)
  
  ⟹18×7=x5+1x5+3
  
  ⟹x5+1x5=18×7−3=123
• 8 years agoHelpfull: Yes(1) No(10)
• (x+1/x)=6
  (x+1/x)² = x²+1/x²+2= 36.
  Therefore, (x²+1/x²) = 34
  Similarly,
  From (x+1/x)³ = 6³ = 216 =>(x³+1/x³) = 198
  Now,
  (x³+1/x³)(x²+1/x²) = 34*198
  (x⁵+1/x⁵)+(x+1/x) = 6732
  (x⁵ + 1/x⁵) = 6732-(x+1/x) = 6732 - 6 = 6726
• 3 years agoHelpfull: Yes(0) No(0)