Question

Rozwiąż równania;
a) 2x-x²=1-(x+3)²=?
b)(x-5)²(x-√3)(x+√3)=?
c)(x+1)²+(x-2)²=2(x-1)(x+1)=?
d)1-4(x+2)²(1-2x)(1+2x)=?
e)(3x-4)²+4(2x+1)²=(5x+2)(5x-2)=?
f)(3x-2x)²+(x+4)(x-4)=5(x-2)²=?
Pilne jak nie wiem co ;P

Answer 1

A) 2x-x²=1-(x+3)²
2x-x²=1-x²+6x+9
2x-x²+x²-6x=9+1
- 4x=10 /:(-4)
x=-10/4
x=-0,4

b) (x-5)²(x-√3)(x+√3)=
( x²-10x+25)(x²-3)
x⁴-3x²-10x³+30x+25x²-75
x⁴-3x²-10x³+30x+25x²=-75
x⁴-10x³+22x²+30x=-75

c) (x+1)²+(x-2)²=2(x-1)(x+1)
x²+2x+1+x²-4x+4=2(x²-1)
x²+2x+1+x²-4x+4=2x²-2
x²+2x+x²-4x-2x²=-2-1-4
-2x=-7/:(-2)
x=7/2

d) 1-4(x+2)²(1-2x)(1+2x)=
1-4(x²+4x+4)(1-4x²)=
1-4(x²-4x⁴+4x-16x³+4-16x²)=
1-4x²+16x⁴-16x+64x³-16+64x²=
16x⁴+64³+60x²-16x-15

e) (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=-4-16-4
-8x=-24/:(-8)
x=3

f) (3x-2x)²+(x+4)(x-4)=5(x-2)²
9x²-12x+4x²+x²-16=5(x²-4x+4)
9x²-12x+4x²+x²-16=5x²-20x+20
9x²-12x+4x²+x²-5x²+20x=20+16
9x²+8x=36