if (a−b)(a+b)=23 then faind a∙b=?


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Question Number 131525 by mathlove last updated on 05/Feb/21

$i f (a - b) (a + b) = 23$ $t h e n f a i n d a \cdot b = ?$
	Answered by mr W last updated on 05/Feb/21

	$n o u n i q u e s o l u t i o n f o r a, b \in R .$ $f o r a, b \in Z :$ $(a - b) (a + b) = 23 = 1 \times 23$ $\Rightarrow a - b = 1$ $\Rightarrow a + b = 23$ $\Rightarrow a = \frac{1 + 23}{2} = 12$ $\Rightarrow b = \frac{23 - 1}{2} = 11$ $\Rightarrow a \times b = 12 \times 11 = 131$ $o r$ $a - b = - 1$ $a + b = - 23$ $\Rightarrow a = - 12$ $\Rightarrow b = - 11$ $\Rightarrow a \times b = 131$
	Commented by mathlove last updated on 05/Feb/21

	$t h a n k s$
	Commented by Rasheed.Sindhi last updated on 06/Feb/21

	$A l s o p o s s i b l e :$ $a + b = 1 \land a - b = 23$ $a = 12, b = - 11$ $a . b = - 132$ $OR$ $a + b = - 1 \land a - b = - 23$ $a = - 12, b = 11$ $a . b = - 132$
	Commented by mr W last updated on 06/Feb/21

	$c o r r e c t s i r! t h a n k s f o r r e m a r k!$
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