6. The sum of a natural number and its
reciprocal is 10/3 . Find the number.
Sol. Let natural number be ‘x’
∴ Its reciprocal is 1/x
From the given condition,
x + 1/x = 10/3
Multiplying by 3x, we get
3x2 + 3 = 10x
∴ 3x2 – 10x + 3 = 0
∴ 3x2 –
9x – x + 3 = 0
∴ 3x (x – 3) – 1 (x
– 3) = 0
∴ (3x – 1) (x – 3) =
0
∴ 3x – 1 = 0 or x –
3 = 0
∴ 3x = 1 or x = 3
∴ x = 1/3 or x = 3
Natural number cannot be a 1/3
∴ x = 3
∴ The required natural number is 3.
