What is the answer to |x^2+3x+2|+|x^2-1|=0 ?

The answer to |x^2+3x+2|+|x^2-1|=0 is x=-1

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|x^2+3x+2|+|x^2-1|=0

x^{2} + 3 x + 2 + x^{2} - 1 = 0

x = - 1

Solution steps

x^{2} + 3 x + 2 + x^{2} - 1 = 0

Factor

x^{2} + 3 x + 2 + x^{2} - 1 : ∣ 1 + x ∣ (∣ 2 + x ∣ + ∣ - 1 + x ∣)

∣ 1 + x ∣ (∣ 2 + x ∣ + ∣ - 1 + x ∣) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

∣ 1 + x ∣ = 0 or ∣ 2 + x ∣ + ∣ - 1 + x ∣ = 0

Solve

∣ 1 + x ∣ = 0 : x = - 1

Solve

∣ 2 + x ∣ + ∣ - 1 + x ∣ = 0 :

No Solution for

x \in R

The solution is

x = - 1

4 (x - 5) = 5

\frac{x}{3} = - 2

\frac{5}{3 i + 1}

3 2^{2}

4 x^{2} - 49 y^{2}

What is the answer to |x^2+3x+2|+|x^2-1|=0 ?
The answer to |x^2+3x+2|+|x^2-1|=0 is x=-1
Solve for x: |x^2+3x+2|+|x^2-1|=0
The solution is x=-1