The equation √x+1-√x-1=√4x-1 has

Question

The equation √x+1-√x-1=√4x-1 has (A) no solution (B) one solution (C) two solutions (D) more than two solutions

Tardigrade Admin · Accepted Answer

Since, √x+1-√x-1=√4x-1 ⇒ (x+1)+(x-1)-2√x2-1=4x-1 ⇒ 1-2x=2√x2-1 ⇒ 1+4x2-4x=4x2-4 4x=5 ⇒ x=(5/4) But it does not satisfy the given equation. Hence, no solution exists.

Q. The equation $x + 1 - x - 1 = 4 x - 1$ has

no solution

one solution

two solutions

more than two solutions

Since, $x + 1 - x - 1 = 4 x - 1$
$\Rightarrow (x + 1) + (x - 1) - 2 x^{2} - 1 = 4 x - 1$
$\Rightarrow 1 - 2 x = 2 x^{2} - 1$
$\Rightarrow 1 + 4 x^{2} - 4 x = 4 x^{2} - 4$
$4 x = 5 \Rightarrow x = \frac{5}{4}$
But it does not satisfy the given equation. Hence, no solution exists.

Q. The equation x+1​−x−1​=4x−1​ has