Topics

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

If \( \Large x=\frac{\sqrt{3}+1}{\sqrt{3}-1}\ and\ y=\frac{\sqrt{3}-1}{\sqrt{3}+1} \), the value of \( \Large x^{2}+y^{2} \) is:

A) 14
B) 13
C) 15
D) 10

Correct Answer:

A) 14

Description for Correct answer:
\( \Large x=\frac{\sqrt{3}+1}{\sqrt{3}-1}\ and\ y=\frac{\sqrt{3}-1}{\sqrt{3}+1} \)

=> Therefore, \( \Large x = \frac{1}{y} \)

\( \Large x = \frac{\sqrt{3}+1}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}-1} \)

= \( \Large \frac{ \left(\sqrt{3}+1\right)^{2} }{3-1} \)

= \( \Large \frac{3+1+2\sqrt{3}}{2} = \frac{4+2\sqrt{3}}{2} \)

= \( \Large \left(2 + \sqrt{3}\right) \)

\( \Large x^{2}= \left(2+\sqrt{3}\right)^{2} = 4+3+4\sqrt{3} \)

= \( \Large 7 + 4\sqrt{3} \)

\( \Large y^{2}=\frac{1}{7+4\sqrt{3}} \times \frac{7-4\sqrt{3}}{7-4\sqrt{3}} \)

\( \Large y^{2} = \frac{7-4\sqrt{3}}{49-48} = \frac{7-4\sqrt{3}}{1} = 7 - 4\sqrt{3} \)

Therefore, \( \Large x^{2}+y^{2}=7+4\sqrt{3}+7-4\sqrt{3} = 14 \)

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

Comments

Similar Questions

1). If \( \Large x=3+\sqrt[2]{2} \), then the value of \( \Large \left(\sqrt{x}-\frac{1}{\sqrt{x}}\right) \) is:

A). 1

B). 2

C). \( \Large 2\sqrt{2} \)

D). \( \Large 3\sqrt{3} \)

2). If p=999, then the value of \( \Large \sqrt[3]{p \left(p^{2}+3p+3\right)+1 } \) is

A). 1000

B). 999

C). 998

D). 1002

3). If \( \Large \frac{a}{b}=\frac{7}{9},\frac{b}{c}=\frac{3}{5} \), then the value of a:b:c

A). 7:9:15

B). 7:9:5

C). 21:35:45

D). 7:3:15

4). If x:y=7:3, then the value of \( \Large \frac{xy+y^{2}}{x^{2}-y^{2}} \) is

A). \( \Large \frac{3}{4} \)

B). \( \Large \frac{4}{3} \)

C). \( \Large \frac{3}{7} \)

D). \( \Large \frac{7}{3} \)

5). If [p] means the greatest positive integer less than or equal to p, then \( \Large \left[ \frac{1}{4} \right]+\left[ 4-\frac{1}{4} \right]+\left[ 3 \right] \) is equal to

A). 4

B). 5

C). 6

D). 7

6). The value of \( \Large \frac{\left(243\right)^{\frac{n}{5}}.3^{2n+1}}{9^{n}.3^{n-1}} \) is

A). 1

B). 9

C). 3

D). \( \Large 3^{n} \)

7). If x=0.5 and y=0.2, then the value of \( \Large \sqrt{0.6} \times \left(3y\right)^{x} \) is equal to

A). 1

B). 0.5

C). 0.6

D). 1.1

8). If \( \Large x^{x\sqrt{x}}= \left(x\sqrt{x}\right)^{x} \) , the x equals

A). \( \Large \frac{4}{9} \)

B). \( \Large \frac{2}{3} \)

C). \( \Large \frac{9}{4} \)

D). \( \Large \frac{3}{2} \)

9). If a=7, b=5 and =3, the value of \( \Large a^{2}+b^{2}+c^{2}-ab-bc-ca \) is

A). 12

B). -12

C). 0

D). 18

10). If \( \Large 7^{x}=\frac{1}{343} \), then the value of x is

A). 3

B). -3

C). \( \Large \frac{1}{3} \)

D). \( \Large \frac{1}{7} \)