Question

Find the fourth proportional to:
a3 - b3, a4 + a2b2 + b4, a - b​

Answer 1

Answer:$x=\frac{(a^{4} +a^{2} b^{2} +b^{4)}}{(a^{2}+ab+ b^{2}) }$

Step-by-step explanation:

Let the fourth proportional to

$a ^{3} - b^{3}$, $a^{4} + a^{2} b^{2} + b^{4}$, $a-b$ be $x$

Then,

= $(a^{3} -b^{3} )$: ($a^{4} +a^{2} b^{2} +b^{4}$) :: (a – b) : x

=>$(a^{3} -b^{3} )$ $x$ =  (a – b) $(a^{4} +a^{2} b^{2} +b^{4})$

=> $x$ = [(a – b). ($a^{4} +a^{2} b^{2} +b^{4}$)] / ($a ^{3} - b^{3}$)

=> $x=\frac{(a-b)(a^{4} +a^{2} b^{2} +b^{4)}}{(a-b)(a^{2}+ab+ b^{2}) }$

=> $x=\frac{(a^{4} +a^{2} b^{2} +b^{4)}}{(a^{2}+ab+ b^{2}) }$