Question

5 si 6. Vă rog!!! repede.

Answer 1

5a) rezulta (√(1-x))²=(x+1)²
1-x=x²+2x+1
x²+2x+1=1-x
x²+2x+x+1-1=0
x²+3x=0
x(x+3)=0
x1=0
x2=-3
S={-3,0}

b)  (3√x+1)²=(x+1)²
9(x+1)=x²+2x+1
9x+9=x²+2x+1
x²+2x+1=9x+9
x²+2x-9x+1-9=0
x²-7x-8=0
Δ=49+32=81
x1=(7-9)/2=-2/2=-1
x2=(7+9)/2=16/2=8
S={-1,8}

c) (√1+x²)²=(x+1)²
1+x²=x²+2x+1
x²-x²-2x+1-1=0
-2x=0
x=0

d)(√4-x²)²=(1-x)²
4-x²=1-2x+x²
-x²-x²+2x+4-1=0
-2x²+2x+3=0    inmultim -1
2x²-2x-3=0
Δ=4+24=28
x1=(-2+2√7)/4=2(-1+√7)/4=(-1+√7)/2
x2=(-1-√7)/2

e) (√x²-3x+2)²=(3-x)²
x²-3x+2=9-12x+x²
x²-x²-3x+12x+2-9=0
9x-7=0
9x=7
x=7/9

f) √x²+9=-x+7
(√x²+9)²=(-x+7)²
x²+9=x²-14x+49
x²-x²+14x+9-49=0
14x-40=0
14x=40
x=40/14=20/7

6a)√x-2=1+√3-x
(√x-2)²=(1+√3-x)²
x-2=1+2√(3-x)+3-x
x+x-2-3=2√(3-x)
2x-5=2√3-x
(2x-5)²=(2√(3-x))²
4x²-20x+25=4(3-x)
4x²-20x+25=12-4x
4x²-20x+4x+25-12=0
4x²-16x+13=0
Δ=256-208=48
x1=(16-4√3)/8=4(4-√3)/8=(4-√3)/2
x2=(4+√3)/2