निम्नलिखित समीकरण को हल कीजिए (3x+1/x+1) + (x+1/3x+1) = 5/2 (x∈R)

Question

निम्नलिखित समीकरण को हल कीजिए

\(\frac{3x+1}{x+1}+\frac{x+1}{3x+1}=\frac{5}{2}\) (x∈R)

Answer 1

2(y² + 1) = 5y

2y² – 5y + 2 = 0

2y² – 4y – y + 2 = 0

2y(y – 2) – 1(y – 2) = 0

(y – 2)(2y – 1) = 0

जब y – 2 = 0 तब जब y = 2

जब 2y – 1 = 0 तब y = 1/2

y = 2 लेने पर, \(\frac{3x+1}{x+1}\) = 2

3x + 1 = 2(x + 1)

3x + 1 = 2x + 2

3x – 2x = 2 – 1

x = 1

y = 1/2 लेने पर, \(\frac{3x+1}{x+1}=\frac{1}{2}\)

2(3x + 1) = x + 1

6x + 2 = x + 1

6x – x = 1 – 2

5x = -1

x = -1/5