The sum of two numbers a and b is 15 and the sum of their reciprocals 1/a and 1/b is 3/10. find the numbers a and b.
Answers
Answered by
67
a+b=15
1/a+1/b=3/10
a+b/ab=3/10
15/ab=3/10
5/ab=1/10
ab=50
(a-b)^2=(a+b)^2-4ab
(a-b)^2=225-200=25
a-b=5
a+b=15
2a=20
a=10
b=15-a
=15-10
=5
1/a+1/b=3/10
a+b/ab=3/10
15/ab=3/10
5/ab=1/10
ab=50
(a-b)^2=(a+b)^2-4ab
(a-b)^2=225-200=25
a-b=5
a+b=15
2a=20
a=10
b=15-a
=15-10
=5
Answered by
44
Hey,
a + b = 15 (equation 1st)
1/a+1/b = 3/10
b+a/ab = 3/10
10a+10b = 3ab
10a + 10b - 3ab = 0 (equation 2nd)
Now, solving both the equations,
In first equation,
a = 15 - b
Substitute b's value in equation second,
10(15-b) + 10b = 3(15-b)*b
150 - 10b + 10b = (45 - 3b) *b
+10b and -10b are cancelled,
150 = 45b - 3b^2
3b^2 - 45b +150 = 0
Solve it to get the answer.
HOPE THIS HELPS YOU BUDDY!!
a + b = 15 (equation 1st)
1/a+1/b = 3/10
b+a/ab = 3/10
10a+10b = 3ab
10a + 10b - 3ab = 0 (equation 2nd)
Now, solving both the equations,
In first equation,
a = 15 - b
Substitute b's value in equation second,
10(15-b) + 10b = 3(15-b)*b
150 - 10b + 10b = (45 - 3b) *b
+10b and -10b are cancelled,
150 = 45b - 3b^2
3b^2 - 45b +150 = 0
Solve it to get the answer.
HOPE THIS HELPS YOU BUDDY!!
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