Question

SOLVE USING COMPONENDO AND DIVIDENDO ​

Answer 1

Answer:

(i). x = 1 ; (ii). x = $\frac{5}{8}$

Step-by-step explanation:

(i). $\frac{3x+\sqrt{9x^2 - 5} }{3x - \sqrt{9x^2 -5} } =5$ ( Function does not exist on - $\frac{\sqrt{5} }{3}$ ≤ x ≤ $\frac{\sqrt{5} }{3}$ )

3x + √(9x² - 5) = 5[3x - √(9x² - 5)]

√(9x² - 5) + 5√(9x² - 5) = 12x ( x ≥ 0)

6√(9x² - 5) = 12x

√(9x² - 5) = 2x

9x² - 5 = 4x²

5x² - 5 = 0

x = 1

(ii). Now is your turn. You can do it.

Function does not exist on  - 0.5 ≤ x ≤ 0.5