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(4/11)n=8/11
We move all terms to the left:
(4/11)n-(8/11)=0
Domain of the equation: 11)n!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
(+4/11)n-(+8/11)=0
We multiply parentheses
4n^2-(+8/11)=0
We get rid of parentheses
4n^2-8/11=0
We multiply all the terms by the denominator
4n^2*11-8=0
Wy multiply elements
44n^2-8=0
a = 44; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·44·(-8)
Δ = 1408
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{22}}{2*44}=\frac{0-8\sqrt{22}}{88} =-\frac{8\sqrt{22}}{88} =-\frac{\sqrt{22}}{11} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{22}}{2*44}=\frac{0+8\sqrt{22}}{88} =\frac{8\sqrt{22}}{88} =\frac{\sqrt{22}}{11} $
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