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[Solved] Equation formula

 
Quadratic Equations
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June 15, 2021 11:37 am
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(@armor)
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Solve the equation \sqrt{x^2+2x-63}+\sqrt{x+9}-\sqrt{7-x}+x+13=0.

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June 15, 2021 11:38 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

The equation has real roots if and only if

  \small x^2+2x-63\geqslant 0,

\small x+9\geqslant 0,

\small 7-x\geqslant 0,

\small \Rightarrow x\geqslant 7   or   \small x\leqslant -9, x\leqslant 7\Rightarrow x=-9   or  \small x=7.

It is easy to obtain that \small x=-9  is a root of the original equation, but \small x=7 is not. Hence, the original equation has a unique root \small x=-9.

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