Question

if the sum of the fraction and its reciprocal is 2 16/21, find the fraction

Answer 1

Refer the attachment!

Answer 2

Answer :-

Fraction is 3/7 or 7/3

Explanation :-

Let the fraction be x

Reciprocal of the fraction = 1/x

Given

Sum of the fraction and reciprocal = 2 16/21

⇒ Fraction + Reciprocal of the fraction = 2 16/21

⇒ x + (1/x) = 58/21

Taking LCM

⇒ (x² + 1)/x = 58/21

By cross multiplication

⇒ 21(x² + 1) = 58(x)

⇒ 21x² + 21 = 58x

⇒ 21x² - 58x + 21 = 0

Comparing with ax² + bx + c = 0 we get

• a = 21

• b = - 58

• c = 21

Discriminant = b² - 4ac = (-58)² - 4(21)(21) = 3364 - 1764 = 1600

Finding roots by quadratic formula

i.e x = {-b ± √(b² - 4ac)}/2a

⇒ x = {-(-58) ± √1600)/2(21)

⇒ x = (58 ± 40)/42

⇒ x = (58 + 40)42 or (58 - 40)/42

⇒ x = 98/42 or 18/42

⇒ x = 7/3 or 3/7

1) If fraction x = 7/3

Reciprocal = 1/x = 1/(7/3) = 3/7

2) If fraction x = 3/7

Reciprocal = 1/x = 1/(3/7) = 7/3

∴ the fraction is 3/7 or 7/3