Question

The product of two numbers is 36 and their sum is 37. What is their difference​

Answer 1

Answer:

AnsWer :

x = 36 , 1.

y = 1 , 36.

SolutioN :

Let,

the number be x and y.

Case 1.

product of two numbers is 36

→ x * y = 36.

Case 2.

their sum is 37.

→ x + y = 37.

Now, Taking Equation ( 1 )

→ x * y = 36.

→ y = 36 / x _____ ( 3 )

Now, Putting the value of x = 36 / y in Equation ( 2 )

→ x + y = 37.

→ x + 36/ x = 37.

→ x² + 36 = 37x.

→ x² - 37x + 36 = 0.

Compare With General Equation.

ax² + bx + c = 0.

Where as,

a = 1.

b = - 37.

c = 36.

→ x² - 36x - x + 36 = 0.

→ x ( x - 36 ) - 1 ( x - 36 ) = 0.

→ ( x - 1 )( x - 36 ) = 0.

Either,

→ x - 1 = 0.

→ x = 1.

Or,

→ x - 36 = 0.

→ x = 36.

Now , putting the value of x = 36 and 1 in Equation ( 3 )

→ y = 36 / x.

→ y = 36 / 36.

→ y = 1.

Or,

→ y = 36 / 1.

→ y = 36.

Therefore, the value of number is x = 36 , 1 and y = 1 , 36.

Answer 2

Answer : 1,36

Step-by-step explanation:

let the both numbers be x and y respectively -

ATQ-

XY = 36. (1)

X +Y = 37 (2)

X = 37 -Y (3) by equation (2)

putting value of x in equation 1

37-y (y) = 36

-y² + 37y - 36 = 0

- ( y² -37y + 36 )= 0

y²- 36y - y + 36 = 0

y ( y - 36) -1 (y - 36 ) = 0

( y-1 ) (y -36) = 0

so, y = 1 or 36

if y =1 then X = 36

if y=36 then X = 1