Solve-the-equation-he-2-she-where-h-e-and-s-are-integers-

Question Number 53770 by Tawa1 last updated on 25/Jan/19

Solve the equation :

{(he)}^{2} = she, where h, e and s are integers .

Answered by mr W last updated on 26/Jan/19

l e t h e = t

t^{2} = 100 s + t

t^{2} - t - 100 s = 0

t = \frac{1 + \sqrt{1 + 400 s}}{2}

1 + 400 s = {(2 n + 1)}^{2}

2 n \times (2 n + 2) = 400 s

\Rightarrow n (n + 1) = 100 s

t h e r e i s o n l y o n e p o s s i b i l i t y :

24 \times 25 = 100 \times 6

i . e . s = 6, n = 24

\Rightarrow t = \frac{1 + 49}{2} = 25 = h e

\Rightarrow {(25)}^{2} = 625

Commented by peter frank last updated on 26/Jan/19

s i r h o w t^{2} = 100 s + t

Commented by Tawa1 last updated on 26/Jan/19

God bless you sir .

Commented by $@ty@m last updated on 26/Jan/19

∵ she i s a 3 d i g i t n u m b e r .

∴ she = 100 s + 10 h + e

\Rightarrow she = 100 s + he

\Rightarrow she = 100 s + t (∵ t = he)

Commented by peter frank last updated on 27/Jan/19

t h a n k s