Question

алгебра тест.............

Answer 1

Ответ: 1) 5

2) 2; 3

3) 1

Объяснение:

1) $x=1+\sqrt{x+11}$

$-\sqrt{x+11} =1-x$

$\sqrt{x+11} = -1+x$

$x+11=x^2-2x+1$

$x+11-x^2+2x-1=0$

$3x+10-x^2=0$

$-x^2+3x+10=0$

$x^2-3x-10=0$

$x^2+2x-5x-10=0$

$x*(x+2)-5(x+2)=0$

$(x+2)*(x-5)=0$

$x+2=0$

$x-5=0$

$x=-2$

$x=5$

$-2=1+\sqrt{-2+11}$

$5=1+\sqrt{5+11}$

$-2=4$

$5=5$

$x\neq -2$

$x=5$

$x=5$

2) $\sqrt{x-2} <1$

$\sqrt{x-2} <1, x\geq 2$

$x-2<1$

$x<1+2$

$x<3, x\geq 2$

x∈ [ 2; 3 )

3) $\sqrt{x} \geq x$

$\sqrt{x} \geq x, x\geq 0$

$\sqrt{x} \geq x, x\geq 0$

$\sqrt{x} \geq x, x< 0$

x∈ [ 0; 1 ] , x ≥ 0

x∈ R , x < 0

x ∈ [ 0; 1 ]

x ∈ ( - ∞ ; 0 )

x ∈ ( - ∞ ; 1 ] , x ≥ 0

x ∈ [ 0 ; 1 ]