Question

(a? - 4a + 3), (a2-a- 6) and (a2-9) find 4th parportion​

Answer 1

Let 4th proportion be x.

Then, we have

(a² - 4a + 3) : (a² - a - 6) :: (a² - 9) : x

$\sf \frac{a^2-4a+3}{a^2-a-6} = \frac{a^2-9}{x}\\\\\implies x = \frac{a^2-9}{a^2-4a+3} \times (a^2-a-6) \\\\\implies x = \frac{(a+3)(a-3)}{a^2-3a-a+3}\times (a^2 -3a+2a-6)\\\\\implies x = \frac{(a+3)(a-3)}{a(a-3)-1(a-3)}\times(a(a-3)+2(a-3))\\\\\implies x = \frac{(a+3)(a-3)}{(a-3)(a-1)}\times(a-3)(a+2)\\\\\implies x = \frac{a+3}{a-1}\times (a-3)(a+2) \\\\\implies x = \frac{(a+3)(a-3)(a+2)}{a-1}\\\\\implies x = \frac{(a^2-9)(a+2)}{a-1}\\\\\implies x = \frac{a^3 + 2a^2 - 9a - 18}{a-1}$

which is the fourth proportion.

Answer 2

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