1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Factorization Method
The sum of tw...
Question
The sum of two numbers is
9
. The sum of their reciprocals is 1/2. Find the sum of squares of the numbers.
Open in App
Solution
⇒
Let one number be
x
, then other number will be
9
−
x
According to the question,
⇒
1
x
+
1
9
−
x
=
1
2
⇒
9
−
x
+
x
x
(
9
−
x
)
=
1
2
⇒
9
9
x
−
x
2
=
1
2
⇒
2
(
9
)
=
9
x
−
x
2
⇒
18
−
=
9
x
−
x
2
⇒
x
2
−
9
x
+
18
=
0
⇒
x
2
−
6
x
−
3
x
+
18
=
0
⇒
x
(
x
−
6
)
−
3
(
x
−
6
)
=
0
$
⇒
(
x
−
6
)
(
x
−
3
)
=
0
⇒
x
−
6
=
0
and
x
−
3
=
0
∴
x
=
6
and
x
=
3
⇒
One number is
6
and other number is
3
⇒
The sum of squares of the numbers
=
(
6
)
2
+
(
3
)
2
=
36
+
9
=
45
Suggest Corrections
0
Similar questions
Q.
The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.
Q.
The sum of two natural numbers is 9 and the sum of their reciprocal is
1
2
. Find the numbers.
Q.
The sum of two natural numbers is 9 and the sum of their reciprocals is
1
2
. Find the numbers. [CBSE 2012]
Q.
Sum of two numbers is 24, and sum of their reciprocals is
1
b
. Find the numbers
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Solving QE by Factorisation
MATHEMATICS
Watch in App
Explore more
Solving a Quadratic Equation by Factorization Method
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app