SATHEE: Theory of Equations 1 Question 29

Theory of Equations 1 Question 29

30. The equation $\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4 x - 1}$ has

(1997C, 2M)

(a) no solution

(b) one solution

(d) more than two solutions

Show Answer

Answer:

Correct Answer: 30. (a)

Solution:

Since,

$\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4 x - 1}$

$\Rightarrow (x + 1) + (x - 1) - 2 \sqrt{x^{2} - 1} = 4 x - 1$

$\Rightarrow 1 - 2 x = 2 \sqrt{x^{2} - 1} \Rightarrow 1 + 4 x^{2} - 4 x = 4 x^{2} - 4$

$\Rightarrow 4 x = 5 \Rightarrow x = \frac{5}{4}$

But it does not satisfy the given equation.

Hence, no solution exists.

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Theory of Equations 1 Question 29

30. The equation x+1−x−1=4x−1 has

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30. The equation $\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4 x - 1}$ has