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If \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=2 \), then x is equal to

A) \( \Large \frac{5}{12} \)
B) \( \Large \frac{12}{5} \)
C) \( \Large \frac{5}{7} \)
D) \( \Large \frac{7}{5} \)

Correct Answer:


B) \( \Large \frac{12}{5} \)

Description for Correct answer:

Given, \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=2 \)

Let \( \Large \sqrt{3+x}=a \ and \ \sqrt{3-x}=b \)

Then, \( \Large \frac{a+b}{a-b}=\frac{2}{1} \)

\( \Large a+b=2a-2b=a=3b \)

On squaring both sides, we get

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

= \( \Large 3+x = 9 \left(3-x\right) \)

= \( \Large 3+x=27-9x \)

= 10x = 24

\( \Large x = \frac{12}{5} \)

Part of solved Linear Equations questions and answers : >> Aptitude >> Linear Equations

Comments

Similar Questions

1). In an examination, a student scores 4 marks for every correct answer and losses 1 mark for every wrong answer. A student attempted all the 200 questions stud and scored 200 marks. Find the number of questions he answered correctly.

A). 82

B). 80

C). 68

D). 60

2). The graphs of ax + by = c, dx + ey = f will be
I. parallel, if the system has no solution.
II. coincident, if the system has finite numbers of solutions.
III. intersecting, if the system has only one solution.
Which of the above statements are correct?

A). Only I and II

B). Only ll and Ill

C). Only I and III

D). I, II and Ill

3). If \( \Large 3^{x+y}=81 \) and \( \Large 81^{x-y}=3 \), then what is the value of x?

A). \( \Large \frac{17}{16} \)

B). \( \Large \frac{17}{8} \)

C). \( \Large \frac{17}{4} \)

D). \( \Large \frac{15}{4} \)

4). Ten chairs and six tables together cost Rs.6200, three chairs and two tables together cost Rs.1900. The cost of 4 chairs and 5 tables is

A). Rs.3000

B). Rs.3300

C). Rs.3500

D). Rs.3800

5). The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has

A). a unique solution x = 1, y=1

B). a unique solution x = 0, y = 4

C). no solution

D). infinite solutions

6). If x+ y - 7 = 0 and 3x + y -13 = 0, then what is \( \Large 4x^{2} + y^{2} + 4xy\) equal to?

A). 75

B). 85

C). 91

D). 100

7). The solution of the equations \( \Large \frac{p}{x}+\frac{q}{y} \ and \ \frac{q}{x}+\frac{p}{y} \) n is

A). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)

B). \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)

C). \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)

D). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)

8). If \( \Large \frac{3}{x+y}+\frac{2}{x-y}=2 \) and \( \Large \frac{9}{x+y}-\frac{4}{x-y}=1 \), then what is the value of \( \Large \frac{x}{y} \)?

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

B). 5

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

D). \( \Large \frac{1}{5} \)

9). If \( \Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y} \) and \( \Large \frac{a}{b}+\frac{b}{a}= x - y \) , then what is the value of x?

A). \( \Large \frac{a+b}{a} \)

B). \( \Large \frac{a+b}{b} \)

C). \( \Large \frac{a-b}{a} \)

D). None of these

10). If \( \Large \frac{x}{2}+\frac{y}{3}=4 \) and \( \Large \frac{2}{x}+\frac{3}{y}=1 \) then what is x + y equal to?

A). 11

B). 10

C). 9

D). 8