If 2((x^2)+1)=5x, find i) x−(1/x) ii) x^3−(1/x^3)

BenoguigoliB 2020-11-08 Answered
If 2((x2)+1)=5x, find i)x(1x)ii)x3(1x3)
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Expert Answer

Corben Pittman
Answered 2020-11-09 Author has 83 answers

We need to first find the value of xx by solving 2(x2+1)=5x.
To solve 2(x2+1)=5x, distribute the 2 to get 2x2+2=5x.
Subtracting 5x5x on both sides then gives 2x25x+2=0.
Factoring would then gives (2x1)(x2)=0.
Now that the equation is in factored form, we can set each factor equal to 0 to find the possible values of x:
2x−1=0 \ x−2=0
2x=1 \ x=2
x=12
Now that we have the possible values of x, we can substitute them into each expression and then simplify to find the values:
i)Ifx=12, then x(1x)=12(11/2)=122=(32)
If x=2, then x(12)=2(12)=32
ii)If x=12,then(x3)(1x3)=(12)3(1(12)3)=18(11/8)=((18)8)=(638)
If x =2, then (x3)(1x3)=(23)(123)=8(18)=638

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