Question

The product of two numbers is 65 and their difference is 8 find these numbers

Answer 1

Step-by-step explanation:

here is your answer and once try to solve it yourself

Answer 2

AnswEr:

$\mathsf{Let\:two\: Numbers\: are \: x \: and \: y.}$

$\sf{Product\: of \: two \: Numbers\: is \: 65.}$

$\sf{And,\: Difference\; is \; 8.}$

$\bigstar\;\:\bold{\underline{\sf{According\:to\: Question}}}$

$\longrightarrow\sf\: x - y = 8$

$\longrightarrow\sf\: x = (y + 8)$

$\rule{150}2$

$\longrightarrow\sf\: x * y = 65$

$\sf{Substituting\:the\:value\:of\:x}$

$\longrightarrow\sf\: y(y + 8) = 65$

$\longrightarrow\sf\: y^2 + 8y - 65 = 0$

$\longrightarrow\sf\: y^2 + 13y - 5y - 65 = 0$

$\longrightarrow\sf\: y(y + 13) -5(y + 13) = 0$

$\longrightarrow\sf\: (y + 13) \;\& \; (y -5)$

$\longrightarrow\sf\: y + 13 = 0$

$\longrightarrow\sf\: y = - 13$

$\rule{150}2$

$\longrightarrow\sf\: y - 5 = 0$

$\longrightarrow\large\boxed{\sf{\blue{ y \:= \:5}}}$

Finding Numbers-

$\longrightarrow\sf\: x = (y + 8)$

$\longrightarrow\sf\: x = -13 + 8$

$\longrightarrow\sf\: x = -5$

If y = 5

$\longrightarrow\sf\: x = (y + 8)$

$\longrightarrow\sf\: x = 5 + 8$

$\longrightarrow\large\boxed{\sf{\blue{x = 13}}}$

So, The Numbers are 5 & 13.