Question

Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.

Answer 1

I hope it is right and helps you

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assume,

Number be 'p'

So,

$\rm \: \: \: \: \: \: \: \: \:p-20=\dfrac{69}{p}$

$\rm \: \: \: \: \: \: \: \: \:p-20-\dfrac{69}{p}=0$

$\rm \: \: \: \: \: \: \: \: \: \dfrac{p^2-20p-69}{p}=0$

p² - 20p - 69 = 0

$\large{\boxed{\sf\:{Splitting\;Middle\;Term}}}$

p² - 20p - 69 = 0

p² - 23p + 3p - 69 = 0

p(p - 23) + 3(p - 23) = 0

(p + 3) (p - 23) = 0

p = -3

Or,

p = 23

$\large{\boxed{\sf\:{Whole\;number\;cannot\;be\;negative}}}$

Hence,

$\Huge{\boxed{\sf\:{Number=23}}}$