Question

If the difference of two numbers is 2 and the product is 80, what are the 2 numbers?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Numbers\:are=(10,8)\:or\:(-8,-10)}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt:\implies Difference \: of \: two \: number = 2 \\ \\ \tt:\implies Product \: of \: two \: number = 80 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies numbers = ?$

• According to given question :

$\circ \: \text{Let \: first \: no. \: be \: x} \\ \\ \circ \: \: \: \: \: \: \: \: \text{second \: no. \: be \: y} \\ \\ \tt: \implies x - y = 2 - - - - - (1) \\ \\ \tt: \implies xy = 80 \\ \\ \tt: \implies x = \frac{80}{y} - - - - - (2) \\ \\ \text{putting \: value \: of \: x \: in \: (1)} \\ \tt: \implies \frac{80}{y} - y = 2 \\ \\ \tt: \implies \frac{80 - {y}^{2} }{y} = 2 \\ \\ \tt: \implies 80 - {y}^{2} = 2y \\ \\ \tt: \implies {y}^{2} + 2y - 80 = 0 \\ \\ \tt: \implies {y}^{2} + 10y - 8y - 80 = 0 \\ \\ \tt: \implies y(y + 10) - 8(y + 10) = 0 \\ \\ \tt: \implies (y - 8)(y + 10) = 0 \\ \\ \green{\tt: \implies y = 8 \: and \: - 10}\\ \\ \text{Putting \: value \: of \: y = 8 \: in \: (1)} \\ \tt: \implies x - 8 = 2 \\ \\ \green{\tt: \implies x = 10} \\ \\ \text{Putting \: value \: of \: y = - 10} \\ \tt: \implies x - ( - 10) = 2 \\ \\ \tt: \implies x + 10 = 2 \\ \\ \green{\tt: \implies x = - 8} \\ \\ \green{\tt \therefore Numbers \: are \: (10, 8) \: or \: ( - 8,- 10)}$

Answer 2

$</p><p>\tt{\huge{\pink{ Hello!!! }}}$

$</p><p>\tt{\red{\boxed{\boxed{\huge{\bullet{Question \: - }}}}}}$

If the difference of two numbers is 2 and the product is 80, what are the 2 numbers?

$\tt{\pink{----------}}$

$</p><p>\tt{\green{\boxed{\boxed{\huge{\bullet{Solution \: - }}}}}}$

Let the two numbers be X and Y ∆ X > Y

X - Y = 2 ..............(1)

XY = 80 .................(2)

Solving ,

$\tt {\green{\therefore{Numbers\:are\:(10,8)\:or\:(−8,−10) }}}$