The sum of two numbers is 135 and their HCF is 27 if their LCM is 162 then find the numbers
Answers
let the number be x and y
x + y = 135
x =135-y............(1)
and we know that
product of two numbers = HCF×LCM
xy = 27×162
put the value of x from (1)
(135-y) y = 27×162
135y-y² = 4374
y² -135y + 4374 = 0
y² - 81y -54y + 4374=0
y(y -81) - 54(y-81) = 0
(y-81)(y-54) = 0
y-81=0, y-54= 0
y=81 , y= 54
put these values in (1)
when y= 81 then , x = 54 and
when y = 54 ,then x=81
hence the two number are
54 and 81
Answer:
Step-by-step explanation:
Let the number be x and y
x + y = 135
x =135-y...(1)
As, product of two numbers = HCF×LCM
xy = 27×162
put the value of x from equ (1)
(135-y) y = 27×162
135y-y² = 4374
y² -135y + 4374 = 0
By splitting the middle term,
y² (- 81y -54y)+ 4374=0
y(y -81) - 54(y-81) = 0
(y-81)(y-54) = 0
y-81=0, y-54= 0
=> y=81 , y= 54
Substitute these values in equ (1)
when y= 81 then , x = 54 and
when y = 54 ,then x=81
Hence the two number are
54 and 81.