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Question Number 86282 by ajfour last updated on 27/Mar/20

Commented by ajfour last updated on 27/Mar/20

$F i n d s / r . (s b e i n g s i d e o f s q u a r e) .$
Commented by Prithwish Sen 1 last updated on 28/Mar/20

$I get$ $x^{3} - 6 x^{2} + 8 x - 4 = 0$ $where x = \frac{s}{r}$
Commented by ajfour last updated on 28/Mar/20

$p l e a s e e x p l a i n h o w y o u r e d u c e d$ $i t t o t h e c u b i c, S i r ?$ $I g e t x \approx 4.38298, y o u r c u b i c$ $t o o f e t c h e s t h e s a m e, b u t i$ $h a d r e s o r t e d t o t r i g o n o m e t r i c$ $w a y . .$
Commented by Prithwish Sen 1 last updated on 28/Mar/20
$b= ((√(s^2 −4sr))/2) ∴ Diagonal AC = AE+EC i.e s(√2)= (√(r^2 +{(√(s^2 −4sr))+(s−r)^2 )) +r(√2) ((s/r)−1)(√2)= (√(1+{(√(((s/r))^2 −4((s/r))))+((s/r)+1)}^2 )) putting (s/r) = x and simplify$
$b = \frac{\sqrt{s^{2} - 4 sr}}{2}$ $∴ Diagonal AC = AE + EC$ $i . e s \sqrt{2} = \sqrt{r^{2} + {\sqrt{s^{2} - 4 sr} + {(s - r)}^{2}} + r \sqrt{2}$ $(\frac{s}{r} - 1) \sqrt{2} = \sqrt{1 + {\sqrt{{(\frac{s}{r})}^{2} - 4 (\frac{s}{r})} + (\frac{s}{r} + 1)}^{2}}$ $putting \frac{s}{r} = x and simplify$
Commented by Prithwish Sen 1 last updated on 28/Mar/20

Commented by ajfour last updated on 28/Mar/20

$T h a n k s S i r . E x c e l l e n t, b r i l l i a n t,$ $n m a g n i f i c i e n t!$
Commented by Prithwish Sen 1 last updated on 28/Mar/20

$welcome$
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