solve over ℝ: (x-1)(x^2+1)=0

⚠ (x-1)(x^2+1)=0 is read as (x-1)*(x^2+1)=0: use (...)*(...) for multiplication, use (...)^(...) for a power

Let's solve in

ℝ

(x - 1) \cdot (x^{2} + 1) = 0

A product is zero if and only if one of its factors is zero: we solve each factor equal to 0

⇥Let's solve in

ℝ

x - 1 = 0

⇥Solution found:

x = 1

⇥Let's solve in

ℝ

x^{2} + 1 = 0

⇥

x^{2} = -1

⇥In ℝ, a square is never negative: no real number has

-1

as its square

⇥Solution:

x \in \emptyset

▶Solution:

x = 1

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