Question

Zadanie o treści: Oblicz: |x^2 - 25| + |x + 5| = 5

Answer 1

|x^2 - 25| + |x + 5| = 5

|(x - 5)(x+5| + |x + 5| = 5

               A                    B                        C                

   x:-∞-----------(-5)----------------(5)--------->∞

x-5       -             -            -             0       +

x+5     -              0           +            +       +

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A:x∈(-∞,-5) ⇒ x²-25-x-5=5

B:x∈[-5,5)  ⇒ -x²+25+x+5=5

C:x∈[5,+∞) ⇒ x²-25+x+5=0

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A: x²-x-35=0

Δ=1+141=141

√Δ=√141≈11,9

x1=(1-√141)/2≈-5.4  OK nalezy do A

x2=(1+√141)/2≈-6.4  NIE nalezy do A

.....................................................................

B: -x²+x+25=0

Δ=1+100=101

√Δ=√101≈10

x1=(-1-√101)/(-2)≈5,52 NIE nalezy do B

x2=(-1+√101)/(-2)≈-4,52 OK nalezy do B

..........................................................................

C: x² - 25+x + 5= 5

x² +x -2 5= 0

Δ=101

x1=(-1-√101)/2=-5,52 NIE nalezy do C

x2=(-1+√101)/2=4,52 NIE nalezy do C

 

ODP

x=(1-√141)/2≈-5.4   ∨ x=(-1+√101)/(-2)≈-4,52

 

 

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