Question

solve x+1/x =25 1/25

Answer 1

Given,

$\frac{x+1}{x}=25\frac{1}{25}\\\\\frac{x+1}{x}=\frac{25\times25+1}{25}\\\\\frac{x+1}{x}=\frac{625+1}{25}\\\\\frac{x+1}{x}=\frac{626}{25}\\\\25(x+1)=626x\\\\25x+25=626x\\\\25=626x-25x\\\\25=601x\\\\x=\frac{25}{601}\\\\Note: a\frac{x}{y}=\frac{ay+x}{y}$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Here, we have

⇒ x + 1/x = 25 (1/25)

⇒ x + 1/x = 25 + 1/25

⇒ x² + 1/x = (25 + 1/25)

⇒ x² + 1 = (25 + 1/25)x

⇒ x² - (25 + 1/25)x + 1 = 0

By using factorization method, we get

⇒ x² - (25 + 1/25)x + 1 = 0

⇒ x² - 25x - 1/25x + 25 × 1/25 = 0

⇒ (x² - 25x) - (x/25 - 25 × 1/25) = 0

⇒ x(x - 25) - 1/25(x - 25) = 0

⇒ (x - 25) (x - 1/25) = 0

⇒ x - 25 = 0 or x - 1/25 = 0

⇒ x = 25, 1/25

Hence, x = 25, 1/25.

Alternative method :-

We have

⇒ x + 1/x = 25 (1/25)

⇒ x + 1x = 25 + 1/25

⇒ x = 25, 1/25     [By comparing two sides]