Question

rezolvati în multimea numerelor reale ecuatiile:​

Answer 1

a) 5×{4×[3×(2×x+1)+1]+1}-44=876

5×{4×[3×(2x+1)+1]+1}=876+44

5×{4×[3×(2x+1)+1]+1}=920

4×[3×(2x+1)+1]+1=920:5

4×[3×(2x+1)+1]+1=184

4×[3×(2x+1)+1]=184-1

4×[3×(2x+1)+1]=183

3×(2x+1)+1=183:4

3×(2x+1)+1=45,75

3×(2x+1)=45,75-1

3×(2x+1)=44,75

2x+1=44,75:3

2x+1=14,91

2x=14,91-1

2x=13,91

x=13,91:2

x=6,955

b)

$\frac{x - 1}{4} + 1 = x - \frac{x - 3}{2} + 0.25 \\ \frac{x - 1}{4} + \frac{1}{1} = \frac{x}{1} - \frac{x - 3}{2} + \frac{25}{10} \\ \frac{5x - 5}{20} + \frac{20}{20} = \frac{20x}{20} - \frac{10x - 30}{20} + \frac{50}{20} \\ (5x - 5 )+ 20 = 20x - (10x - 30 ) + 50 \\ 5x - 5 + 20 = 20x - 10x + 30 + 50 \\ 5x - 20x + 10x = 30 + 50 - 20 \\ - 5x = 60 \\ x = 60 \div ( - 5) \\ x = - 12$

c)

$\frac{1}{ \sqrt{3} } \times (x - 2) + \sqrt{48} = \sqrt{12} \\ \frac{ \sqrt{3} }{3} \times (x - 2) + 4 \sqrt{3} = 2 \sqrt{3} \\ \frac{ \sqrt{3} }{3} \times \frac{3x - 6}{3} + \frac{12 \sqrt{3} }{3} = \frac{6 \sqrt{3} }{3} \\ \sqrt{3} \times (3x - 6) + 12 \sqrt{3} = 6 \sqrt{3} \\ \sqrt{3} \times (3x - 6) = 6 \sqrt{3} - 12 \sqrt{3} \\ \sqrt{3} \times (3x - 6) = - 6 \sqrt{3} \\ 3x - 6 = - 6 \sqrt{3} \div \sqrt{3} \\ 3x - 6 = - 6 \\ 3x = - 6 + 6 \\ 3x = 0 \\ x = 0 \div 3 \\ x = 0$

d) nu exista ecuatii echivalente