Question

Proszę o pomoc z matematyki, Liceum - 2 klasa.

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Answer 1

8. (1-4x)(1+4x)=1²-(4x)² = 1-16x²

(2x²-3)² = 4x⁴-12x²+9

(x+2/3)³=x³+3x²*2/3 +3x*4/9+ 8/27 = x³+2x²+4/3x + 8/27

(5-3x)³=125-75*3x+15*9x²-27x³=125-225x+135x²-27x³

(2-x)(2+x)(4+x²)=(4-x²)(4+x²)=16-x⁴

(√2x-1)(2x²-1)(√2x+1)=(2-1)(2x²-1)=2x²-1

(2x+1)(4x²-2x+1)=8x³-4x+2x+4x²-2x+1=8x³+4x²-4x+1

(x-2)(x²+2x+4)(x³+8)=(x-2)(x+2)²(x³+8)=(x-2)(x+2)(x+2)(x³+8)=(x²-4)(x+2)(x³+8)=
(x³+2x²-4x-8)(x³+8)=x⁶+8x³+2x⁵+16x²-4x⁴-32x-8x³-64=x⁶+2x⁵-4x⁴+16x²-32x-64

 

9. -x³+4x²+x-1

a=-(3)³+4*3²+3-1=-27+32+2=7

b=-(-1)³+4*(-1)²-1-1=1+4-2=3

c=-(0)³+4*0²+0-1=0+0+0-1=-1

 

10. -px³+3x²+x-6q

4=-p(-1)³+3(-1)²-1-6q

3=-p(0)³+3(0)²-0-6q

 

4=p+3-1-6q

3=0+0-0-6q

 

3=-6q   -> q=-1/2

4=p+2-6q  -> 2=p-6q  -> p = 2+3=5

 

11. 6x³+x²-4x+1

W(-3)=6*(-3)³+(-3)²-4(-3)+1=6*(-27)+9+12+1  = -162+22 = -140

W(-1)=6*(-1)³+(-1)²-4(-1)+1=-6+1+4+1=-6+6=0

W(1)=6*1+1-4+1=6+2-4=4

 

-1 jest pierwiastkiem.

 

12. x³+3x²+(m²-2m)x+2

0=(-2)³+3(-2)²+(m²-2m)*-2 +2

0= -8+12-2m²+4m+2

0=6-2m²+4m

-6=-2m²+4m

-6=-2(m²-2m)

3=m²-2m

m²-2m-3=0

Δ= (-2)²-4*(-3)=16

m1= 2+4 / 2= 3

m2 = 2-4 / 2 = -1