the product of two numbers is 91 and their arithmetic mean is 10. find the two numbers.
Answers
Answered by
54
Let two numbers are X and Y .
Mean of two numbers = 10
X + Y /2 = 10
X + Y = 20 ---------(1)
Product of two numbers = 91
X × Y = 91
X = ( 91/Y ) ---------(2)
Putting the value of X in equation (1) , we get
X + Y = 91
91 / Y + Y = 20
91 + Y² = 20Y
Y² - 20Y + 91 = 0
Y² - 13Y - 7Y + 91 = 0
Y( Y - 13 ) -7 ( Y - 13 ) = 0
( Y - 13 ) ( Y - 7 ) = 0
( Y - 13 ) = 0 or ( Y -7 ) = 0
Y = 13 or Y = 7
Putting Y = 13 in equation (2) , we get
X = 91/Y = 91/13 = 7.
Hence,
two numbers are 13 and 7.
Mean of two numbers = 10
X + Y /2 = 10
X + Y = 20 ---------(1)
Product of two numbers = 91
X × Y = 91
X = ( 91/Y ) ---------(2)
Putting the value of X in equation (1) , we get
X + Y = 91
91 / Y + Y = 20
91 + Y² = 20Y
Y² - 20Y + 91 = 0
Y² - 13Y - 7Y + 91 = 0
Y( Y - 13 ) -7 ( Y - 13 ) = 0
( Y - 13 ) ( Y - 7 ) = 0
( Y - 13 ) = 0 or ( Y -7 ) = 0
Y = 13 or Y = 7
Putting Y = 13 in equation (2) , we get
X = 91/Y = 91/13 = 7.
Hence,
two numbers are 13 and 7.
Answered by
24
Step-by-step explanation:
ok hopes that it helps you a lot thank me and mark me as branliest
Attachments:
Similar questions