Question

Rozwiąż nierówności. Dam naj!

Answer 1

B) zal1 xe(-niesk, 0)
-36x+x³≤0
x(-36+x²)≤0
x(x-6)(x+6)≤0
xe(-niesk,-6)
zal2 xe<0,+niesk)
x(36-x²)≤0
xe(6,+niesk)
i)|x(x²-6)|≤x²
zal1 xe(-niesk, -√6)u(0,√6)
-x(x²-6)≤x²
-x³-x²-6x≤0
-x(x²-x-6)≤0
xe(-4,-√6)
zal2 xe<-√6,0>u<√6,+niesk)
x³-6x-x²≤0
x(x²-x-6)≤0
xe<√6,3>
k) zal1 xe(-niesk, -1)
-(x+1)²(x+1)+49(x+1)≤0
(x+1)(-x²-2x-1+49)≤0
(x+1)(-x²-2x+48)≤0
-(x+1)(x+8)(x-6)≤0
xe(-8,-1)
zal2 xe<-1,+niesk)
(x+1)(x+1)²-49(x+1)≤0
(x+1)(x²+2x+1-49)≤0
(x+1)(x²+2x-48)≤0
(x+8)(x-6)(x+1)≤0
xe<-1,6>
l) zal1 xe(-niesk,0)
-x³+5x+2≥0
-(x+2)(-x+√2+1)(x+√2-1)≥0
xe(-niesk, -2>u<1-√2>
zal2 xe<0,+niesk)
x³-5x+2≥0
(x-2)(x+1+√2)(x-√2+2)≥0
xe<0,√2-1>u<2,+niesk)