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2n-(1/n)=100
We move all terms to the left:
2n-(1/n)-(100)=0
Domain of the equation: n)!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
2n-(+1/n)-100=0
We get rid of parentheses
2n-1/n-100=0
We multiply all the terms by the denominator
2n*n-100*n-1=0
We add all the numbers together, and all the variables
-100n+2n*n-1=0
Wy multiply elements
2n^2-100n-1=0
a = 2; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·2·(-1)
Δ = 10008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10008}=\sqrt{36*278}=\sqrt{36}*\sqrt{278}=6\sqrt{278}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-6\sqrt{278}}{2*2}=\frac{100-6\sqrt{278}}{4} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+6\sqrt{278}}{2*2}=\frac{100+6\sqrt{278}}{4} $
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