Question

a)6x(5x+3)=18x
b)81-2(x-1)la puterea a 2-a=51
c)(x+2)la puterea a 2-a+(x-2)la puterea a 2-a=80
d)3xla p.a2-a -4=4-3x la a 2-a
e)4x la puterea a 2-a=(2+radical din3)la puterea a 2-a
f)2x la puterea a 2-a=(2+radical din 2)la puterea a 2-a

Answer 1

a)30x+18=18x
30x-18x=-18
12x=-18
x=-18/12=-9/4
x=-2,25

b)81-2(x²-2x+1)=51
81-2x²+4x-2-51=0
-2x²+4x+28=0    inmultim-1
2(x²-2x-14)=0
x²-2x-14=0
Δ=4+56=60
x1=(2-2√15)/2=2(1-√15)/2=1-√15
x2=1+√15

c)x²+4x+4+x²-4x+4=80
2x²+8=80
2x²=80-8
2x²=72
x²=72/2
x²=36
x1=√36=6
x2=-√36=-6

d)3x²-4=4-3x²
3x²+3x²=4+4
6x²=8
x²=8/6=4/3
x1=√4/3=2/√3=2√3/3
x2=-2√3/3

e)4x²=(2+√3)²
4x²=4+4√3+2
4x²=6+4√3
x²=2(3+2√3)/4=(3+2√3)/2
x1=√(3+2√3)/√2=(√6+2√6)/2=3√6/2
x2=-3√6/2

f)2x²=(2+√2)²
2x²=4+4√2+2
2x²=6+4√2
x²=2(3+2√2)/2=3+2√2
x1=√(3+2√2)
x2=-√(3+2√2)