Question

Rozwiąż Równania:

a) (x+1)²=x²
b) (x+6)²=(x-2)²
c) x(2x-1)=2(x+2)²
d) (3x-4)²+4(2x+1)²=(5x+2)(5x-2)
e) (3-2x)²+(x+4)(x-3)=5(x-2)²+7

Answer 1

(x+1)²=x²
x²+1=x²
1=0
-
(x+6)²=(x-2)²
x²+36=x²+4
x²-x²=4-36
0=-32
-
x(2x-1)=2(x+2)²
2x²-x=2(x²+4)
2x²-x=2x²+8
2x²-x-2x²=8
-x=8
x=-8
-
(3x-4)²+4(2x+1)²=(5x+2)(5x-2)
9x²+16+4(4x²+1)=25x²-10x+10x-4
9x²+16+16x²+4=25x²-4
25x²-25x²=-4-16-4
0=-24
-
(3-2x)²+(x+4)(x-3)=5(x-2)²+7
9-4x²+x²-3x+4x-12=5(x²+4)+7
9-4x²+x²-3x+4x-12=5x²+27
x-8x²=12+27-9
x-8x²=30 tego zrobic nie umiem ale jak bym mial robic to bym tak zostawil

Answer 2

A) (x+1)²=x²
x²+2x+1=x²
x²+2x-x²= -1
2x=-1
x= -½

b) (x+6)²=(x-2)²
x²+12x+36= x²-4x+4
x²+12x - x²+4x= 4-36
16x= -32
x= -2

c) x(2x-1)=2(x+2)²
2x²-x = 2(x²+4x+4)
2x²-x = 2x²+8x+8
2x²-x -2x²-8x = 8
-9x= 8
x= 8/9

d) (3x-4)²+4(2x+1)²=(5x+2)(5x-2)
9x²-24x+16 + 4(4x²+4x+1) = 25x²-4
9x²-24x+16 + 16x² +16x+4= 25x²-4
9x²-24x + 16x² +16x - 25x² = -4 -4 -16
-8x= -24
x= 3


e) (3-2x)²+(x+4)(x-3)=5(x-2)²+7
9-12x +4x² + x²-3x+4x-12= 5(x²-4x+4) + 7
9-12x +4x² + x²-3x+4x-12= 5x²- 20x +20 +7
-12x +4x² + x²-3x+4x -5x² + 20x= 20 +7 -9 +12
9x= 30
x= 30/9
x= 3⅓