The sum of two positive number is 9 and the sum pf the squares is 45. Find the numbers
Answers
Answered by
1
x + 1 + X + 2 = 9
2 X + 3= 9
x=6÷2
x=3
Answered by
3
Let m and n be the numbers
Then m+n=9
m^2+n^2=45
(m+n)^2= 81
m^2 + n^2+ 2mn=81
45+2mn=81
2mn=81-45=36
mn=18
(m-n)^2=(m+n)^2 - 4mn
=81-4x18
=81-72
=9
So m+n=9—(1)
m-n=3———(2)
Adding (1) and (2),
2m=12
m=6
From (1),
n=9-m=9-6=3
So the numbers are 3 and 6
Then m+n=9
m^2+n^2=45
(m+n)^2= 81
m^2 + n^2+ 2mn=81
45+2mn=81
2mn=81-45=36
mn=18
(m-n)^2=(m+n)^2 - 4mn
=81-4x18
=81-72
=9
So m+n=9—(1)
m-n=3———(2)
Adding (1) and (2),
2m=12
m=6
From (1),
n=9-m=9-6=3
So the numbers are 3 and 6
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