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Question

If x+1/x =5 then find
1. x​​​​​​2+1/x​​​​​​2
2. x​​​​​​4 + 1/x^2

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Solution

We know (a+b)^2= a^2+2ab+b^2
given that x+1/x=5
squaring both LHS & RHS gives (x+1/x)^2=5^2
using the identity;
(x^2)+(2*x*1/x)+(1/x)^2=25
(x^2)+2+(1/x)=25-2
(x^2)+(1/x)^2=23 ■

now squaring the above result (x^2)^2+(2*(x^2)*(1/x^2))+(1/x)^2=23^2
(x^4)+2+(1/x)^4=529
(x^4)+(1/x)^4=527■


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