Question

Va rog frumos sa mă ajutați la aceste exerciții.
Vreau doar ce știți!

Answer 1

1. a) 4x-1=5

4x=5+1

4x=6

x=\frac{6}{4} (simplifici cu 2 fractia)

x=\frac{3}{2} ⇒ S=\frac{3}{2}

b) \frac{3}{4}x-1\frac{1}{6}=0

\frac{3x}{4}-\frac{7}{6}=0 (amplifici prima fractie cu 3, iar a doua cu 2)

9x-14=0

9x=0+14

9x=14

x=\frac{14}{9}, x∈Z ⇒ S=Ф

c) √5x-√30=0

√5x=0+√30

√5x=√30

x=√30/√5

x=√6, x∈Q⇒ S=Ф

2. a) 2x+1=3

2x=3-1

2x=2

x=\frac{2}{2}

x=1⇒ S={1}

b) 4x-6=2(x-3)

4x-6=2x-6

4x-2x=-6+6

2x=0

x=\frac{0}{2}

x=0⇒ S={0}

c) √18x+3/√2=0

3√2x+3/√2=0 (rationalizezi fractia cu √2)

3√2x+3√2/2=0

3√2x=-3√2/2 (imparti ecuatia cu 3√2)

x=-\frac{1}{2} ⇒ S={-\frac{1}{2} }

3. a) 4x²-1=0

4x²=0+1

4x²=1

x²=\frac{1}{4}

x=√1/√4

x=\frac{1}{2}

b) |4x-1|=1

4x-1=1

4x=1+1

4x=2

x=\frac{2}{4}

x=\frac{1}{2}

4x+1=1

4x=1-1

4x=0

x=0

c) 4x²=9

x²=\frac{9}{4}

x=√9/√4

x=\frac{3}{2}

4. a) -\frac{3}{4}x +√11=0 (amplifici √11 cu 4)

-3x+4√11=0

-3x=-4√11

x=-4√11/-3

x=4√11/3

b) \sqrt{(x-\sqrt{2})^{2} =2√2

x-√2=2√2

x=2√2+√2

x=3√2

c) \frac{3x-1}{2} -3(x-1)=\frac{x+1}{3}

\frac{3x-1}{2} -3x+3=\frac{x+1}{3} (inmultesti prima fractie cu 3, a doua ecuatie cu 6 si a treia fractie cu 2)

3(3x-1)-18x+18=2(x+1)

9x-3-18x+18=2x+2

-9x+15=2x+2

-9x-2x=2-15

-11x=-13 (inmultesti ecuatia cu -1)

11x=13

x=\frac{13}{11}