If \( \Large x = 7-4\sqrt{3} \), then the value of \( \Large x+\frac{1}{x} \)


A) \( \Large 3\sqrt{3} \)

B) \( \Large 8\sqrt{3} \)

C) \( \Large 14+8\sqrt{3} \)

D) 14

Correct Answer:
D) 14

Description for Correct answer:
\( \Large x = 7 - 4\sqrt{3} \)

\( \Large \frac{1}{x} => \frac{1}{7-4\sqrt{3}} \)

By ratonalisation,

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

= \( \Large \frac{7+4\sqrt{3}}{49-48}= 7 + 4\sqrt{3} \)

Therefore, \( \Large x+\frac{1}{x} = 7 - 4\sqrt{3} + 7 + 4\sqrt{3} \)

= 14

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








Comments

No comments available




Similar Questions
1). If \( \Large \frac{a}{b}=\frac{2}{3}\ and\ \frac{b}{c}=\frac{4}{5} \) , then the ratio \( \Large \frac{a+b}{b+c} \) equal to:
A). \( \Large \frac{20}{27} \)
B). \( \Large \frac{27}{20} \)
C). \( \Large \frac{6}{8} \)
D). \( \Large \frac{8}{6} \)
-- View Answer
2). If \( \Large a\ast b=2 \left(a+b\right) \), then \( \Large 5\ast 2 \) is equal to:
A). 3
B). 10
C). 14
D). 20
-- View Answer
3). If \( \Large \frac{2a+b}{a+4b}=3 \), then find the value of \( \Large \frac{a+b}{a+2b} \)
A). \( \Large \frac{5}{9} \)
B). \( \Large \frac{2}{7} \)
C). \( \Large \frac{10}{9} \)
D). \( \Large \frac{10}{7} \)
-- View Answer
4). If \( \Large a\ast b=a+b+ab \), then \( \Large 3\ast 4-2\ast 3 \) is equal to:
A). 6
B). 8
C). 10
D). 12
-- View Answer
5). If \( \Large x \circledast y = 3x+2y \), then \( \Large 2 \circledast 3+3 \circledast 4 \) is equal to
A). 18
B). 29
C). 32
D). 38
-- View Answer


6). If a : b = 2 : 3 and b : c = 4 : 5, find \( \Large a^{2} : b^{2} : bc \)
A). 4 : 9 : 45
B). 16 : 36 : 45
C). 16 : 36 : 20
D). 4 : 36 : 40
-- View Answer
7). If \( \Large A : B = \frac{1}{2} : \frac{3}{8},\ B : C = \frac{1}{3} : \frac{5}{9},\ C : D = \frac{5}{6} : \frac{3}{4} \), then find the ratio of A : B : C : D
A). 6 : 4 : 8 : 10
B). 6 : 8 : 9 : 10
C). 8 : 6 : 10 : 9
D). 4 : 6 : 8 : 10
-- View Answer
8). If A : B : C = 2 : 3 : 4, then \( \Large \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \) is equal to
A). 8 : 9 : 16
B). 8 : 9 : 12
C). 8 : 9 : 24
D). 4 : 9 : 16
-- View Answer
9). A : B - 1 : 2, B : C =3 : 4, C : D = 5 : 6, find D : C : B : A
A). 6 : 5 : 4 : 2
B). 6 : 3 : 2 : 1
C). 6 : 4 : 2 : 1
D). 48 : 40 : 30 : 15
-- View Answer
10). If \( \Large \frac{2a-5b}{3a+6b}=\frac{4}{7} \), then a:b is equal to
A). 21 : 36
B). 2 : 56
C). 59 : 2
D). 36 : 21
-- View Answer