The sum of a number and its reciprocal is 10/3. If the number is x, then x + 1/x = 10/3, i.e. 3x^2 - 10x + 3 = 0. Solve by completing the square to find the number (give the larger value).

Question

Accepted Answer

3. Divide by 3: x^2 - 10/3x + 1 = 0. (x - 5/3)^2 = 25/9 - 1 = 16/9, x - 5/3 = +/-4/3, x = 3 or x = 1/3. Larger is 3.

The sum of a number and its reciprocal is $\frac{10}{3}$ .
If the number is $x$ , then $x + \frac{1}{x} = \frac{10}{3}$ , i.e. $3 x^{2} - 10 x + 3 = 0$ .
Solve by completing the square to find the number (give the larger value).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Completing the Square practice

The sum of a number and its reciprocal is 310​.If the number is x, then x+x1​=310​, i.e. 3x2−10x+3=0.Solve by completing the square to find the number (give the larger value).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Completing the Square practice

The sum of a number and its reciprocal is $\frac{10}{3}$ .
If the number is $x$ , then $x + \frac{1}{x} = \frac{10}{3}$ , i.e. $3 x^{2} - 10 x + 3 = 0$ .
Solve by completing the square to find the number (give the larger value).