Respuesta :

revolve

Answer:

[tex]\sqrt{(n-m)(n+m)}[/tex] & [tex]-\sqrt{(n-m)(n+m)}[/tex]

Step-by-step explanation:

1) Subtract [tex]m^{2}[/tex] from both sides. This should leave you with [tex]x^{2}=n^{2}-m^{2}[/tex].

2) Square root both sides. This should leave you with [tex]x=\sqrt{n^2-m^2}[/tex] & [tex]x=-\sqrt{n^2-m^2}[/tex].

You can stop here if this is what the problem is asking for. However, it is not fully simplified.

3) Factor the equation. This should leave you with [tex]\sqrt{(n-m)(n+m)}[/tex] & [tex]-\sqrt{(n-m)(n+m)}[/tex].

Answer:

[tex]\boxed{\left \{ {{\sqrt{(n-m)(m+n)}} \atop {-\sqrt{(n-m)(m+n)}}} \right.}[/tex]

Solution Steps:

- Steps using the quadratic formula -

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1.)  Subtract n² from both sides:

  • [tex]n^2-n^2=0[/tex]
  • [tex]m^2-n^2=m^2-n^2[/tex]

2.) Rewrite:

This equation is in standard form: ax² + bx² + c = 0. Substitute 1 for a, 0 for b, and (m-n) (m+n) for c in the quadratic formula, [tex]\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}[/tex]:

  • [tex]x^2+m^2-n^2=0[/tex]

   2.a)  Turns into:

  • [tex]x=\frac{0\frac{+}{}\sqrt{0^2-4(m-n)(m+n)}}{2}[/tex]

3.) Square 0:

  • [tex]0^2=0[/tex] (Also means it Cancels out.)

4.)  Take the square root of −4(m−n)(m+n):

This just means combine them by squaring.

  • [tex]-4^2=2[/tex] (Half it, don't square it.)
  • [tex](m-n)(m+n)^2=(n^2-m^2)[/tex]

   4a.)  Our equation should look like this now:

  • [tex]x=\frac{0\frac{+}{}2\sqrt{(n^2-m^2)}}{2}[/tex]

5.)  Solve the equation using ±:

Solve the equation [tex]x=\frac{0\frac{+}{}2\sqrt{(n^2-m^2)}}{2}[/tex]:

   5a.) Solve the equation when ± is plus:

  • [tex]x=\sqrt{(n-m)(m+n)}[/tex]

   5b.) Solve the equation when ± is minus:

  • [tex]x=-\sqrt{(n-m)(m+n)}[/tex]

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Hope this helps!

If you have any questions, or need help with anything else, feel free to ask! I'm happy to help!

- TotallyNotTrillex -