Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

The sum of a number and its reciprocal is \( \Large \frac{10}{3} \), then the numbers are

A) \( \Large 3, \frac{1}{3} \)
B) \( \Large 3, -\frac{1}{3} \)
C) \( \Large -3, \frac{1}{3} \)
D) \( \Large -3, -\frac{1}{3} \)

Correct Answer:

A) \( \Large 3, \frac{1}{3} \)

Description for Correct answer:

Let the numbers be x and \( \Large \frac{1}{x} \)

Then, \( \Large x + \frac{1}{x} = \frac{10}{3} \)

=> \( \Large \frac{x^{2} + 1}{x} = \frac{10}{3} \)

=> \( \Large 3x^{2} - 10x + 3 = 0 \)

=> \( \Large 3x^{2} - 9x - x + 3 = 0 \)

=> \( \Large 3x \left(x - 3\right) - 1 \left(x-3\right) = 0 \)

=> \( \Large \left(3x - 1\right) \left(x - 3\right) = 0 \)

\( \Large x = \frac{1}{3}, x = 3 \)

Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations

Comments

Similar Questions

1). In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was

A). \( \Large x^{2}+10x+9=0 \)

B). \( \Large x^{2}-10x+16=0 \)

C). \( \Large x^{2}-10x+9=0 \)

D). None of the above.

2). The difference in the roots of the equation \( \Large 2x^{2}-11x+5=0 \) is

A). 4.5

B). 4

C). 3.5

D). 3

3). If one roots of the equation is reciprocal of the other, then which one of the following is correct?

A). a = b

B). b = c

C). ac = 1

D). a = c

4). Number of solutions of the equation \( \Large \sqrt{x^{2}-x+1}+\frac{1}{\sqrt{x^{2}-x+1}}=2-x^{2} \) is

A). 0

B). 1

C). 2

D). 4

5). If \( \Large x = \sqrt{\frac{\sqrt{5}+1}{\sqrt{5}-1}} \), then \( \Large x^{2}-x-1 \) is equal to

A). 0

B). 1

C). 2

D). 5

6). If one of the roots of the equation \( \Large x^{2}-bx+c=0 \) is the square of the other, then which of the following option is correct?

A). \( \Large b^{2} = 3bc+c^{2}+c \)

B). \( \Large c^{3} = 3bc+b^{2}+b \)

C). \( \Large 3bc = c^{3}+b^{2}+b \)

D). \( \Large 3bc = c^{3}+b^{3}+b^{2} \)

7). Two students A and B solve an equation of the form \( \Large x^{2}+px+q=0 \). A starts with a wrong value of p and obtains the roots as 2 and 6. B starts with a wrong value of q and gets the roots as 2 and -9. What are the correct roots of the equation?

A). 3 and -4

B). -3 and -4

C). -3 and 4

D). 3 and 4

8). 7059 - 2350 + 1936 = x 50

A). 123.6

B). 132.3

C). 132.6

D). 132.9

9). If \( \Large \sqrt{2} \) = 1.4142, then the value of \( \Large \frac{7}{4 + \sqrt{2}} \) is

A). 3.5858

B). 4.4142

C). 1.2929

D). 1.5858

10). What is 786 times of 964 ?

A). 759276

B). 749844

C). 75416

D). 757704