3/y2=6

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Solution for 3/y2=6 equation:



3/y2=6
We move all terms to the left:
3/y2-(6)=0
Domain of the equation: y2!=0
y^2!=0/
y^2!=√0
y!=0
y∈R
We multiply all the terms by the denominator
-6*y2+3=0
We add all the numbers together, and all the variables
-6y^2+3=0
a = -6; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-6)·3
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-6}=\frac{0-6\sqrt{2}}{-12} =-\frac{6\sqrt{2}}{-12} =-\frac{\sqrt{2}}{-2} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-6}=\frac{0+6\sqrt{2}}{-12} =\frac{6\sqrt{2}}{-12} =\frac{\sqrt{2}}{-2} $

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