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[Solved] Equation with roots

 
Quadratic Equations
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June 15, 2021 11:31 am
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(@armor)
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Let  a,b  be two real numbers,  |a|>0,   and the equation  ||x-a|-b|=5  has three distinct roots, find the value of b. 

 

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June 15, 2021 11:31 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

The equation \small ||x-a|-b|=5  is equivalent to \small |x-a|-b=\pm 5\Leftrightarrow |x-a|=b\pm 5.

The equation has three distinct roots if and only if \small b-5=0,  that is \small b=5 and the roots are \small x=a, x=a\pm 10

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