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Question Number 112795 by I want to learn more last updated on 09/Sep/20

Commented by MJS_new last updated on 10/Sep/20

$trying 10 ⩽ N ⩽ 99 we get$ $N \in {12, 24, 36, 48, 75, 81}$
	Answered by Rasheed.Sindhi last updated on 10/Sep/20

	$(10 t + u) (t + u) = k^{2}$ $10 t^{2} + 11 u t + u^{2} = k^{2}$ $O n e c a s e :$ $t + u = 10 t + u \Rightarrow t = 0$ $B u t t ⩾ 10$ $t h e b i g g e s t t w o - d i g i t n u m b e r i s 99$ $99 (9 + 9) = k^{2}$ $k^{2} ⩽ 1782$ $k ⩽ 42$ $T h e s m a l l e s t t w o - d i g i t n u m b e r i s 10$ $10 (1 + 0) = 10$ $k^{2} ⩾ 10$ $k ⩾ 4$ $4 ⩽ k ⩽ 42$ $C o n t i n u e$ $10 t^{2} + 11 u t + u^{2} - k^{2} = 0$
	Commented by I want to learn more last updated on 09/Sep/20

	$What is the final sir please$
	Commented by I want to learn more last updated on 11/Sep/20

	$Thanks sir$
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