What are the roots of this eq Solutionw12 2 ka 2 ml2 2g

What are the roots of this eq?

Solution

w1,2 = { ( 2 ka ^2 / ml^2 + 2g / l ) + - sqrt { ( 4ka^4 / ml^4 + 4g^2 / l^2 + 8ka^2g / ml^3 - 8ka^2g / ml^3 - 4g^2 / l^2 )} / 2

w 1,2 = { ( 2 ka ^2 / ml^2 + 2g / l ) + - sqrt ( 4ka^4 / ml^4 ) } / 2

w1,2 = { ( 2 ka ^2 / ml^2 + 2g / l ) + - 2 ka^2 / ml^2 } / 2

w1 = 2g/l / 2 = g/l

w2 = (4ka^2 / ml^2 + 2g/l )/2 = (2ka^2 / ml^2 + g/l )

 What are the roots of this eq? Solutionw1,2 = { ( 2 ka ^2 / ml^2 + 2g / l ) + - sqrt { ( 4ka^4 / ml^4 + 4g^2 / l^2 + 8ka^2g / ml^3 - 8ka^2g / ml^3 - 4g^2 / l^2

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