Question

the sum of two number is 19 and the product is 60 what are the numbers​

Answer 1

Answer:

One number is x, and the other number is (19-x).

[x-(19-x)](x)= 60

Answer 2

Answer

The numbers are 15 and 4

$\bf\large\underline{Given}$

• Sum of two numbers is 19
• The product of two numbers is 60

$\bf\large\underline{To \: Find}$

• The numbers

$\bf\large\underline{Solution}$

Let the numbers be x and y respectively

$\sf \underline{ \underline{According \: to \: question : }}$

$\sf \implies x + y = 19 \\\\ \sf\implies x = 19 - y \dashrightarrow (1)$

$\sf \underline{ \underline{Again \: by \: question : }}$

$\sf\implies xy = 60 \\\\ \sf\underline{\underline{Putting \ the \ of \ x \ from \ (1) :}} \\\\ \sf\implies (19-y)y = 60 \\\\ \sf\implies 19y - y^{2} - 60=0 \\\\ \sf\implies y^{2} - 19y + 60 = 0 \\\\ \sf\implies y^{2} - 15y - 4y + 60 = 0 \\\\ \sf\implies y(y - 15) - 4(y-15) = 0 \\\\ \sf\implies (y-15)(y-4) = 0$

Therefore ,

$\sf y - 15= 0 \: \: and \: \: y - 4 = 0 \\ \\ \implies \sf y = 15 \: \: and \implies y = 4$

$\sf \underline{ \underline{Putting \: the \: value \: of \: y \: in \: (1)</p><p>}}$

$\sf x = 19 - 15 \: \: and \: \: x = 19 - 4 \\ \\ \implies \sf x = 4 \: \: and \: \implies x = 15$

Therefore , the required numbers are either 15 and 4 or 4 and 15