- #1

martinrandau

- 9

- 0

sqrt(x^2-x-10) = 10 + sqrt(x^2 - 11x)

Solve for x.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter martinrandau
- Start date

- #1

martinrandau

- 9

- 0

sqrt(x^2-x-10) = 10 + sqrt(x^2 - 11x)

Solve for x.

- #2

TD

Homework Helper

- 1,022

- 0

Note: by squaring you may introduce new solutions. You'll have to check those, each expression under a root can't be negative, so cancel out false solutions.

- #3

bomba923

- 760

- 0

Just expanding on what TD said,

[tex] \sqrt {x^2 - x - 10} = 10 + \sqrt {x^2 - 11x} \Rightarrow x^2 - x - 10 = 100 + 20\sqrt {x^2 - 11x} + x^2 - 11x \Rightarrow [/tex]

[tex] x - 11 = 2\sqrt {x^2 - 11x} \Rightarrow 3x^2 - 22x - 121 = 0 \Rightarrow x = \frac{{22 \pm \sqrt {22^2 + 1452} }}{6} \Rightarrow x = \left\{ { - \frac{{11}}{3},11} \right\} [/tex]

However, you probably want *[tex] \boxed{x = 11} [/tex]* because [itex] -11 / 3 [/itex] won't work!

Why? Because squaring [itex] x - 11 = 2\sqrt {x^2 - 11x} [/itex] introduces false solutions!

[tex] \sqrt {x^2 - x - 10} = 10 + \sqrt {x^2 - 11x} \Rightarrow x^2 - x - 10 = 100 + 20\sqrt {x^2 - 11x} + x^2 - 11x \Rightarrow [/tex]

[tex] x - 11 = 2\sqrt {x^2 - 11x} \Rightarrow 3x^2 - 22x - 121 = 0 \Rightarrow x = \frac{{22 \pm \sqrt {22^2 + 1452} }}{6} \Rightarrow x = \left\{ { - \frac{{11}}{3},11} \right\} [/tex]

However, you probably want *[tex] \boxed{x = 11} [/tex]* because [itex] -11 / 3 [/itex] won't work!

Why? Because squaring [itex] x - 11 = 2\sqrt {x^2 - 11x} [/itex] introduces false solutions!

Last edited:

Share:

- Replies
- 8

- Views
- 553

- Replies
- 1

- Views
- 945

- Last Post

- Replies
- 9

- Views
- 609

- Last Post

- Replies
- 3

- Views
- 527

- Last Post

- Replies
- 4

- Views
- 1K

- Replies
- 6

- Views
- 884

- Last Post

- Replies
- 6

- Views
- 740

- Replies
- 0

- Views
- 442

- Replies
- 68

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 401