Question

Product of two no is 270 and their difference is 3 the what are the numbers

Answer 1

Answer:

18 and 15  

Step-by-step explanation:

Let the two numbers be x and y

x * y = 270   ⇒  x = $\frac{270}{y}$   ...   (i)

x - y = 3

$\frac{270}{y}$ - y = 3

$\frac{270 - y^{2} }{y}$ = 3

270 - y² = 3y

y² + 3y - 270 = 0   ...   (ii)

Factor pairs of 270 are (1, 270) , (2,135),  (3, 90) , (5, 54) ,(6, 45), (9, 30) , (10, 27) (15, 18)

3y can be written as 18y - 15y

Equation (ii) can be written as,

y² + 18y  - 15y - 270 = 0    

y(y + 18) - 15(y + 18) = 0

y + 18 = 0 or y - 15 = 0

y = -18 or y = 15

As, y cannot be negative, y = 15

Using  y = 15 in (i),

x = $\frac{270}{15} = 18$

∴ The two numbers are 18 and 15