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(x + 1/x) = 6 the value of ( x5 + 1/x5 ) = ?
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- (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 - 9 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
- 9 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 - 9 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
- 9 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 - 9 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 - 4 years agoHelpfull: Yes(0) No(0)
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