Question
a certain positive number is equal to nine-tenths of the sum of the number and its reciprocal. find the number
Answers
Reiny
(9/10)x + 1/x = x
times 10
9x + 10/x = 10x
times x
9x^2 + 10 = 10x^2
x^2 = 10
x = √10
check:
1/√10
= 1/√10 *√10/√10 = √10/10
so
(9/10)√10 + 1/√10
= (9/10)√10 + √10/10
= 10√10/10 = √10
times 10
9x + 10/x = 10x
times x
9x^2 + 10 = 10x^2
x^2 = 10
x = √10
check:
1/√10
= 1/√10 *√10/√10 = √10/10
so
(9/10)√10 + 1/√10
= (9/10)√10 + √10/10
= 10√10/10 = √10