Question

Rozwiąż:

a)(x+√3)(2+√3)=4+2√3
b)-5+x²≥0
c)x²+2x-3≥-2x-3
d)√(6x+4)²≥11
e)(x²+2x)²-x²=0
f)x⁴-x²-12=0
g)(2-x)(3x+1)(2x-3)>0

Answer 1

A)(x+√3)(2+√3)=4+2√3
2x+x√3+2√3+3=4+2√3
2x+x√3=-1
x(2+√3)=-1 /: (2+√3)
x= -1/2+√3
x= -2-√3/ 12

b)-5+x²≥0
x²≥5 lub x≥-5

c)x²+2x-3≥-2x-3
x²+2x≥0

d)√(6x+4)²≥11
6x+4≥11
6x≥7 /:6
x≥7/6

e)(x²+2x)²-x²=0
x²+4x³+4x²-x²=0
4x³+4x²=0 /:4
x³+x²=0 /√
√x+x=0

f)x⁴-x²-12=0
x⁴-x²=12 /√
x²-x=4√3

g)(2-x)(3x+1)(2x-3)>0
6x+2+4x-6-3x²-x-2x²+3x+6x²-9x+2x-3>0
5x+x²>7
5(x+x²)>7 / :5
x+x²>7/5