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Algebra Level 3

Consider the following:

  • Let S1{ S }_{ 1 } be the sum of the roots of the equation 4x2+58x=04{ x }^{ 2 }+5-8x=0

  • Let S2{ S }_{ 2 } be the sum of the roots of the equation log6(x2)+log6(x+3)=2\log _{ 6 }{ \left( x-2 \right) } +\log _{ 6 }{ \left( x+3 \right) } =2

  • Let S3{ S }_{ 3 } be the sum of the roots of the equation x7x3=37x3x-\cfrac { 7 }{ x-3 } =3-\cfrac { 7 }{ x-3 }

  • Let S4{ S }_{ 4 } be the sum of the roots of the equation 4x+2x=14x+\sqrt { 2x } =1

Then find the value of ZZ where Z=S1+S2+S3+S4Z={ S }_{ 1 }+{ S }_{ 2 }+{ S }_{ 3 }+{ S }_{ 4 }.


AYWC?

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