Question

Rozwiąż nierówność:

a) (x-2)(x+2)+5 > (x-6)²

b) (x-1)²-2(x-3) > (x+√5)(x-√5)

c) (8z+3)(8z-3)+(6z+2)² < (10z+1)(10z-1)+4(2z+7)

d) (10p+9)²-(8p+7)² ≥ (6p+5)²+5

Proszę na dziś. Daje Naj.

Answer 1

a) (x-2)(x+2)+5 > (x-6)²

x²+2x-2x-4+5 > x²-12x+36

x²+1 > x²-12x+36

12x > 35

x > 2¹¹/₁₂

x∈(2¹¹/₁₂;∞)

 

b) (x-1)²-2(x-3) > (x+√5)(x-√5)

x²-2x+1-2x+6 > x²-5

-4x > -12

x < 3

x∈(-∞;3)

 

c) (8z+3)(8z-3)+(6z+2)² < (10z+1)(10z-1)+4(2z+7)

64z²-9+36z²+24z+4 < 100z²-1+8z+28

-5+24z < 27+8z

16z < 32

z < 2

z∈(-∞;2)

 

d) (10p+9)²-(8p+7)² ≥ (6p+5)²+5

100p²+180p+81-64p²-112p-49 ≥ 36p²+60p+25+5

68p+32 ≥ 60p+30

8p ≥ -2

p ≥ -¼

p∈<-¼;∞)

Answer 2

a)

x^2+2x-2x-4+5>x^2-12x+36

x^2-x^2+12x>-1+36

12x>35   /:12

x>35/12

 

b)

x^2-2x+1-2x+6>x^2-5

-4x>-5-7

-4x>-12   /:-4

x<3

c)

64z^2-9+36z^2+24z+4<100z^2-1+8z+28

24z-8z<5-1+28

16z<32  /:16

z<2

 

d)

100p^2+180p+81-64p^2-112p-49>=36p^2+60p+25+5

180p-112p-60p>=30-81+49

8p>=-2  /:8

p>=-2/8

p>=-1/4