Question

find the fourth proportional to: (a2 - ab + b2),(a3 +b3) and (a-b)​

Answer 1

The fourth proportional to: (a2 - ab + b2),(a3 +b3) and (a-b)​ is $\left ( \textrm{a-b} \right )^{2}$

Step-by-step explanation:

Given  $(\textrm{a}^{2}-\textrm{ab}+\textrm{b}^{2}) :(\textrm{a}^{3}-\textrm{b}^{3})::\left ( \textrm{a}-\textrm{b} \right ):\textrm{X}$

$\Rightarrow \dfrac{\textrm{a}^{2}-\textrm{ab}+\textrm{b}^{2}}{\textrm{a}^{3} -\textrm{b}^{3} } =\dfrac{\textrm{a-b}}{\textrm{X} }$

$\Rightarrow \dfrac{1}{\textrm{a-b}}=\dfrac{\textrm{a-b}}{\textrm{X}}$

$\Rightarrow \textrm{X}=\left ( \textrm{a-b} \right )^{2}$

So Fourth Proportional i s $\left ( \textrm{a-b} \right )^{2}$

Answer 2

The answer is a² -b ². ( just expand a³ +b³)

(a³+b³) = (a² -ab +b²)(a+b)