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Mathematics

Grade10

Easy

Question

Find the two consecutive integers whose product is 72. Select all the options that apply.

(-9 and -8) (8 and 9)

8 and 9
9 and 9
-9 and 8
-8 and 9

The correct answer is: (-9 and -8) (8 and 9)

8 and 9

Let n represent one integer. Then n+1 represents the next integer.
$n left parenthesis n plus 1 right parenthesis equals 72 space space space space space T h e space p r o d u c t space o f space t h e space t w o space i n t e g e r s space i s space 72 table attributes columnalign right end attributes row cell n squared plus n equals 72 equals end cell 0 blank row cell n squared plus n minus 72 end cell cell equals 0 end cell blank row cell left parenthesis n plus 9 right parenthesis left parenthesis n minus 8 right parenthesis end cell cell equals 0 end cell blank row cell n plus 9 equals 0 end cell cell text or end text end cell cell n minus 8 equals 0 end cell row cell n equals negative 9 end cell cell text or end text end cell cell n equals 8 end cell end table$
$text If end text n equals negative 9 text , then end text n plus 1 equals negative 9 plus 1 equals negative 8 text . If end text n equals 8 text , then end text n plus 1 equals 8 plus 1 equals 9 text . Thus the end text$
consecutive integers are -9 and -8 or 8 and 9.

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