Question

Please solve this if someone knows it

Answer 1

Answer:

Don't know the answer sorry.

Answer 2

Answer:

(i) Shown that the equation reduces to $x^2 + x - 12 = 0$

(ii) x = -4  or x = 3

(iii) The larger number is 4 and the smaller number is 3.

Step-by-step explanation:

(i) According to the given conditions:

$\frac{12}{x} - \frac{12}{x + 1} = 1$

$=> 12(\frac{1}{x} - \frac{1}{x + 1} ) = 1$

$=> 12[\frac{x + 1 - x}{x(x + 1)} ] = 1$

$=> 12 = x(x + 1)$  [multiplying both sides by x(x + 1)]

$=>x^2 + x - 12 = 0$  

(ii) $x^2 + x - 12 = 0$

$=>x^2 + 4x - 3x - 12 = 0$

$=>x(x + 4) - 3(x + 4) = 0$

$=>(x + 4)(x - 3) = 0$

∴ x = -4  or x = 3

(iii) Negative value of x will make the numbers negative, while it is given that the numbers are positive.  Therefore, we take x = 3.

Hence, the larger number $=\frac{12}{x}$ $= \frac{12}{3}$$= 4$

And the smaller number $=\frac{12}{x + 1}$  $= \frac{12}{4}$ $= 3$