If a number plus its reciprocal equals 10/3, find the number. Class 9

If a number plus its reciprocal equals 10/3, find the number. Class 9

Question 1.

If a number plus its reciprocal equals $\frac{10}{3}$, find the number. Class 9

Solution:

Let the number be x.

Then its reciprocal = $\frac{1}{x}$

According to the given condition,

$x+\frac{1}{x}=\frac{10}{3}$

Multiplying both sides by 3x, we get

3x² + 3 = 10x

∴ 3x² - 10x + 3 = 0

∴ 3 (x² - $\frac{10}{3} x$ + 1) = 0

∴ x² - $\frac{10}{3} x$ + 1 = 0

Since (-3) + $\left(-\frac{1}{3}\right)=-\frac{10}{3}$ and

(-3) × $\left(-\frac{1}{3}\right)$ = 1.

the numbers are -3 and $-\frac{1}{3}$.

∴ (x - 3) (x $-\frac{1}{3}$) = 0

∴ (x - 3) = 0 or (x $-\frac{1}{3}$) = 0

∴ x = 3 or x = $\frac{1}{3}$

Thus, the number is 3 or $\frac{1}{3}$