if x^3 + 1/x^3 =110, then x+1/x

1.	if x^3 + 1/x^3 =110, then x+1/x
Answer» x^3+1/x^3=110 (x+1/x)^3=x^3+1/x^3+3(x+1/x) (x+1/x)^3=110+3 (x+1/x) Let(x+1/x)=a eq … 1 So, a^3=110+3a a^3-3a-110=0 P (a)=a^3-3a-110 PUT a=5 P (5)=(5)^3-3 (5)-110=125-15-110 125-125=0 P (5)=0 1st factor =(a-5) Write (a-5) three times and put the value according to polynomial a^2(a-5)+5a(a-5)+22(a-5) (a-5)(a^2+5a+22) If (a-5)=0 or (a^2+5a+22)=0 (a-5)=>x+1/x-5=0 from eq1 x+1/x=5 ans

Answer»

x^3+1/x^3=110

(x+1/x)^3=x^3+1/x^3+3(x+1/x)

(x+1/x)^3=110+3 (x+1/x)

Let(x+1/x)=a eq … 1 So,

a^3=110+3a

a^3-3a-110=0

P (a)=a^3-3a-110

PUT a=5

P (5)=(5)^3-3 (5)-110=125-15-110

125-125=0

P (5)=0

1st factor =(a-5)

Write (a-5) three times and put the value according to polynomial

a^2(a-5)+5a(a-5)+22(a-5)

(a-5)(a^2+5a+22)

If (a-5)=0 or (a^2+5a+22)=0

(a-5)=>x+1/x-5=0 from eq1

x+1/x=5 ans

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