Question

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√х+1=8-2х

Answer 1

$sqrt{x+1}=8-2x\ =========================\ left { {{x+1 geq 0} atop {8-2x geq 0}} right. \ left { {{x geq -1} atop {-2x geq -8}} right. \ left { {{x geq -1} atop {x leq 4}} right. Rightarrow xin [-1;4] \ =========================\ ( sqrt{x+1})^2=(8-2x)^2\ x+1=64-32x+4x^2\ 64-32x+4x^2-x-1=0\ 4x^2-33x+63=0\ D=b^2-4ac=(-33)^2-4cdot4cdot63=1089-1008=81=9^2\ x_1= frac{33+9}{8} = 5.25 notin [-1;4] \ x_2= frac{33-9}{8} = 3$

Ответ: x = 3