The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has
- no solution
- one solution
- two solutions
- more than two solutions
The Correct Option is A
Solution and Explanation
$\Rightarrow\, \, \, \, \, \, (x+1)+(x-1)-2\sqrt{x^2-1}=4x-1$
$\Rightarrow\hspace25mm1-2x=2\sqrt{x^2-1}$
$\Rightarrow\, \, \, \, \, \, 1+4x^2-4x=4x^2-4$
$\hspace25mm 4x=5 \Rightarrow x=\frac{5}{4}$
But it does not satisfy the given equation.
Hence, no solution exists.
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
