Question

The sum of of two number is 25 and their product is 100 find the numbers​

Answer 1

AnswEr :

Numbers will be 5 and 20.

Explanation :

Let the Numbers be a and b.

• (a + b) = 25
• (a × b) = 100

» a + b = 25

» a = 25 - b

➟ (a × b) = 100 [ Given ]

➟ (25 - b) × b = 100

➟ 25b - b² = 100

➟ b² - 25b + 100 = 0

➟ b² - 20b - 5b + 100 = 0

➟ b(b - 20) - 5(b - 20) = 0

➟ (b - 5)(b - 20) = 0

➟ b = 5 or, b = 20

Putting the Value of b in (a = 25 - b)

➟ a = 25 - b

➟ a = (25 - 5) or, a = (25 - 20)

➟ a = 20 or, a = 5

჻ So the Numbers will be 5 and 20.

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Let , the two numbers be x and y

According to the question ,

$\to$x + y = 25

x = 25 - y ----- eq (i)

$\to$xy = 100 ----- eq (ii)

Put the value of x = 25 - y in equation (ii)

$\to \sf (25 - y) × y = 100 \\ \\ \to \sf </p><p></p><p>25y - {y}^{2} = 100 \\ \\ \to \sf </p><p> {y}^{2} - 25 y + 100 = 0 \\ \\ \to \sf </p><p> {y}^{2} - 20y - 5y + 100 = 0 \\ \\ \to \sf </p><p>y(y- 20) - 5(y - 20) = 0 \\ \\ \to \sf </p><p>(y - 5)(y- 20) = 0 \\ \\ \to \sf</p><p>y = 5 \: \: or \: \: y = 20$

Putting the value of y = 5 or 20 in equation (i)

$\to \sf a = 25 - b \\ \\ \to \sf</p><p></p><p>a = (25 - 5) \: \: or \: \: a = (25 - 20)</p><p> \\ \\ \to \sf</p><p>a = 20 \: \: or \: \: a = 5</p><p>$

$\therefore$ the numbers are 5 and 20