Question

To zadanie polega na "wyliczeniu"ile wynosi X
a)(x+1)²+2x+2=(x-1)²-4
b)2x(x+3)+(x+4)²=(x-1)(3x+2)+3
c)(x-2)²=(x+3)(x-3)-(0,5x+1)
d)(√2x-1)(√2x+1)-(2x+1)²+(3x-2)²=5x²-12
e)5(x-1)-(x-2)²=6x-(x+3)²
f)(x-5)²-(x-2)(x+2)=x²-(x+1)(x-1)
g)x√2=√32+√2
h)5x√3-√27=x√12

Answer 1

A) x²+1+2x+2=x²-1-4
x²+3+2x-x²+5=0
2x+8=0
Δ=4
√Δ=2

x1=0
x2=0

b)
2x²+6x+x²+16=3x²+2x-3x-3
2x²+6x+x²+16-3x²-2x+3x+3=0
7x-19=0

Δ=49
√Δ=7

x1=0
x2=0

Answer 2

A)(x+1)²+2x+2=(x-1)²-4
x²+2x+1+2x+2=x²-2x+1-4 |-x²
4x+3=-2x-3
2x=0
x=0

b)2x(x+3)+(x+4)²=(x-1)(3x+2)+3
2x²+6x+x²+8x+16=3x²+2x-3x-2+3
3x²+14x+16=3x²-x+1 |-3x²
14x+16=-x+1 |+x
15x=1-16
15x=-15
x=-1

c)(x-2)²=(x+3)(x-3)-(0,5x+1)
x²-4x+4=x²-9-0,5x-1 |-x²
-4x+4=-10-0,5x
-4x+0,5x=-10-4
-3,5x=-14
x=4

d)(√2x-1)(√2x+1)-(2x+1)²+(3x-2)²=5x²-12
2x-1-(4x²+4x+1)+(9x²-12x+4)=5x²-12
2x-1-4x²-4x-1+9x²-12x+4=5x²-12
-2-14x+5x²=5x²-12 |-5x²
-2x-14=-12
-2x=-12+14
-2x=2
x=-1

e)5(x-1)-(x-2)²=6x-(x+3)²
5x-5-(x²-4x+4)=6x-(x²+6x+9)
5x-5-x²+4x-4=6x-x²-6x-9
9x-9-x²=-9-x² |-x²
9x-9=-9 |+9
9x=0
x=0

f)(x-5)²-(x-2)(x+2)=x²-(x+1)(x-1)
x²-10x+25-(x²-4)=x²-(x²-1)
x²-10x+25-x²+4=x²-x²+1
10x+29=1 |-29
10x=28
x=2,8

g)x√2=√32+√2
x√2=4√2+√2
x√2=5√2 |*√2
2x=10
x=5

h)5x√3-√27=x√12
5x√3-3√3=2x√3 |*√3
15x-9=6x |-15x
-9=-9x
x=1