The sum of a number and it's reciprocal is 21/30. Find the number.
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Answered by
4
Let the number be X.
Reciprocal of X = ( 1/X ).
Given : Sum of number + Reciprocal of number = 21/30
=> X + 1/X = 21/30
=> X² + 1 / X = 21/30
=> 30 ( X² + 1 ) = 21X
=> 30X² + 30 = 21X
=> 30X² - 21X + 30 = 0
=> 3( 10X² - 7X + 10 ) = 0
=> 10X² - 7X + 10 = 0
X = -b + √B²-4ac / 2a
X = -(-7) + √(-7)² -4×10×10/2×10
X = 7 + √-351/20
Reciprocal of X = ( 1/X ).
Given : Sum of number + Reciprocal of number = 21/30
=> X + 1/X = 21/30
=> X² + 1 / X = 21/30
=> 30 ( X² + 1 ) = 21X
=> 30X² + 30 = 21X
=> 30X² - 21X + 30 = 0
=> 3( 10X² - 7X + 10 ) = 0
=> 10X² - 7X + 10 = 0
X = -b + √B²-4ac / 2a
X = -(-7) + √(-7)² -4×10×10/2×10
X = 7 + √-351/20
Answered by
1
Given: Sum of a number and its reciprocal is 21/30.
To find: The number.
Answer:
Let us take the number as x.
Therefore its reciprocal will be 1/x.
Sum of the number and its reciprocal ⇒ x + 1/x
x + 1/x = 21/30
30(x + 1) = 21x
30x + 30 = 21x
30x - 21x = -30
9x = -30
x = -30/9
x = -3.3
Hope it helps :)
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