Question

Rozwiąż równania:
a) (x+1)²=x²
b) (2x-3)²=4x²-3x
c) (x+6)²=(x-2)²
d) 4x(x-20)=(2x+4)²
e) x(2x-1)=2(x+2)²
f) 2x-x²=1-(x+3)²
g)(x-5)²=(x-√3)(x+√3)
h)(x+1)²+(x-2)²=2(x-1)(x+1)
i)(3x-4)²+4(2x+1)²=(5x+2)(5x-2)
j)1-4(x+2)²=(1-2x)(1+2x)
k)(3-2x)²+(x+4)(x-3)=5(x-2)²+7
l)2(x-0,2)²=x²+(x+0,1)²
PROSZE O WSZYSTKIE OBLICZENIA !!!!

Answer 1

A (x+1)²=x²
x²+2*x*1+1²=x²
2x=-1
x=-1/2
b (2x-3)²=4x²-3x
2x²-2*2x*3+3²=4x²-3x
4x²-12x+9=4x²-3x
-9x=-9
x=1
c(x+6)²=(x-2)²
x²+2*x*6+6²=x²-2*x*2+2²
x²+12x+36=x²-4x+4
16x=-32
x=-2
d 4x(x-20)=(2x+4)²
4x²-80x=2x²+2*2x*4+4²
4x²-80x=4x²+16x+16
-96x=16
x=-16/96
x=-1/6
e) x(2x-1)=2(x+2)²
2x²-x=2(x²+2*x*2+2²)
2x²-x=2x²+4x+4
3x=4
x=3/4
f) 2x-x²=1-(x+3)²
2x-x²=1-(x²+2*x*3+3²)
2x-x²=1-x²-6x-9
2x=1-6x-9
8x=-8
x=-1
g)(x-5)²=(x-√3)(x+√3)
x²-2*x*5+5²=x²-3
-10x+25=-3
-10x=-28
x=28/10
x=2 i 8/10
h)(x+1)²+(x-2)²=2(x-1)(x+1)
x²+2*x*1+1²+x²-2*x*2+2²=2(x²-1)
x²+2x+1+x²-4x+4=2x²-2
2x-4x=-3
-2x=-3
x=3/2= 1 i 1/2
i)(3x-4)²+4(2x+1)²=(5x+2)(5x-2)
to mi nie wychodzi;/
3x²-2*3x*4+4²=4(2X²-2*2*1+1²=25x²-4
9x²-24x+16+4(4x²-4x+1)=25x²-4
-24x-16x=-16-4-4
-40x=-24
x=24/40
x=3/5
j)1-4(x+2)²=(1-2x)(1+2x)
1-4(x²+2*x*2+2²)=1-4x²
1-4(x²-4x-4)=1-4x²
1-4x²-16x-16=1-4x²
1-16x-16=1
-16x=16
x=-1
k)(3-2x)²+(x+4)(x-3)=5(x-2)²+7
3²-2*3*2x+2x²+x²-12=5(x²-2*x*2+2²)+7
9-12x+4x²+x²-12=5x²-20x+20+7
9-12x-12=-20x+20+7
8x=-9+12+20+7
8x=30
x=30/8
x=3i 3/4
l)2(x-0,2)²=x²+(x+0,1)²
nie umiem;/

a tam dzie kwadraty zniknęły tzn że sie skrócily

Answer 2

A (x+1)²=x²
x²+2*x*1+1²=x²
2x=-1
x=-1/2

b (2x-3)²=4x²-3x
2x²-2*2x*3+3²=4x²-3x
4x²-12x+9=4x²-3x
-9x=-9
x=1

c(x+6)²=(x-2)²
x²+2*x*6+6²=x²-2*x*2+2²
x²+12x+36=x²-4x+4
16x=-32
x=-2

d 4x(x-20)=(2x+4)²
4x²-80x=2x²+2*2x*4+4²
4x²-80x=4x²+16x+16
-96x=16
x=-16/96
x=-1/6

e) x(2x-1)=2(x+2)²
2x²-x=2(x²+2*x*2+2²)
2x²-x=2x²+4x+4
3x=4
x=3/4

f) 2x-x²=1-(x+3)²
2x-x²=1-(x²+2*x*3+3²)
2x-x²=1-x²-6x-9
2x=1-6x-9
8x=-8
x=-1

g)(x-5)²=(x-√3)(x+√3)
x²-2*x*5+5²=x²-3
-10x+25=-3
-10x=-28
x=28/10
x=2 i 8/10

h)(x+1)²+(x-2)²=2(x-1)(x+1)
x²+2*x*1+1²+x²-2*x*2+2²=2(x²-1)
x²+2x+1+x²-4x+4=2x²-2
2x-4x=-3
-2x=-3
x=3/2= 1 i 1/2

i)(3x-4)²+4(2x+1)²=(5x+2)(5x-2)
9x²-16+4(4x²+1)=25x²-4
9x²-16+16x²+4=25x²-4
9x²+16x²-25x²=16-4+4
0=16

j)1-4(x+2)²=(1-2x)(1+2x)
1-4(x²+2*x*2+2²)=1-4x²
1-4(x²-4x-4)=1-4x²
1-4x²-16x-16=1-4x²
1-16x-16=1
-16x=16
x=-1

k)(3-2x)²+(x+4)(x-3)=5(x-2)²+7
3²-2*3*2x+2x²+x²-12=5(x²-2*x*2+2²)+7
9-12x+4x²+x²-12=5x²-20x+20+7
9-12x-12=-20x+20+7
8x=-9+12+20+7
8x=30
x=30/8
x=3i 3/4

l)2(x-0,2)²=x²+(x+0,1)²
2(x²+0,04)=x²+x²+0,01
2x²+0,08= x²+x²+0,01
2x²-x²-x²=0,01-0,08
0=0,07

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