Question

the product of two consecutive integers is 72. Find all solutions.

Answer 1

$\huge\boxed{\texttt{\fcolorbox{red}{aqua}{Hey Mate!!!}}}$
$<b><i><font face=Copper black size=4 color=blue>$
Here is your answer
Let the two consecutive integers are x and x+1

ATQ
$x(x + 1) = 72 \\ \\ {x}^{2} + x = 72 \\ \\ {x}^{2} + x - 72 = 0 \\ \\ {x}^{2} + 9x - 8x - 72 = 0 \\ \\ x(x + 9) - 8(x + 9) = 0 \\ \\ (x + 9)(x - 8) = 0 \\ \\ x = 8 \: \: and - 9 \\ \\ as \:number \: is \: not \: negative \: so \\ \\ x = 8 \\ \\ other \: is \\ 8 + 1 = 9$
Therefore Two consecutive integers are 8 and 9

$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}}$

$\huge\boxed{\texttt{\fcolorbox{Red}{yellow}{Be brainly!!!}}}$

$<marquee>$
$\huge\bf{\red{\huge{\bf{@.....rajeev378}}}}$