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Algebra Level 3

Consider the following:

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

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

  • Let S 3 { S }_{ 3 } be the sum of the roots of the equation x − 7 x − 3 = 3 − 7 x − 3 x-\cfrac { 7 }{ x-3 } =3-\cfrac { 7 }{ x-3 }

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

Then find the value of Z Z where Z = S 1 + S 2 + S 3 + S 4 Z={ S }_{ 1 }+{ S }_{ 2 }+{ S }_{ 3 }+{ S }_{ 4 } .

AYWC?

1.25 10.625 4.5 1.5 none of these 7.575

Soumo Mukherjee by Soumo Mukherjee , 25, India

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2 solutions

Soumo Mukherjee
Jan 13, 2015

  • Sum of roots of the equation 4 x 2 + 5 − 8 x = 0 4{ x }^{ 2 }+5-8x=0 is 2 2 .

  • − 7 -7 is not a root of the equation log ⁡ 6 ( x − 2 ) + log ⁡ 6 ( x + 3 ) = 0 \log _{ 6 }{ \left( x-2 \right) } +\log _{ 6 }{ \left( x+3 \right) } =0 This equation becomes meaningless at − 7 -7 . This equation has 6 6 as the only root.

  • The equation x − 7 x − 3 = 3 − 7 x − 3 x-\cfrac { 7 }{ x-3 } =3-\cfrac { 7 }{ x-3 } has no roots. At x = 3 x=3 this equation becomes undefined.

  • The equation 4 x + 2 x = 1 4x+\sqrt { 2x } =1 has only one root that is 1 8 \cfrac { 1 }{ 8 } . This equation becomes meaningless at 1 2 \cfrac { 1 }{ 2 } .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

This is my solution after the correction. XD

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Correction: The third equation has no root s it will be un defined at x = 3 x=3

Sualeh Asif - 6 years, 5 months ago

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Thanksss :D

Winardi Emmanuel Setiawan - 6 years, 5 months ago

I don't think -7 is considered as a root for the second equation as it will render log(x-2) undefined, so I think that 6 is the only root for equation 2.

Martin Kok - 5 years, 11 months ago

You got the right answer by fluke, my dear friend. Check equation2 instead of − 30 -30 it must be − 42 -42 . In equation3, 3 3 makes the equation undefined.

The rest you did correct. :)

Soumo Mukherjee - 6 years, 5 months ago

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Oh, right... Thanks for the correction.. :D

Winardi Emmanuel Setiawan - 6 years, 5 months ago

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