- Consider the given equation: \[\frac{\sqrt{p+x}+\sqrt{p-x}}{\sqrt{p+x}-\sqrt{p-x}} = p\]
- To eliminate the square roots, multiply both sides by \[\sqrt{p+x}-\sqrt{p-x}\]: \[(\sqrt{p+x}+\sqrt{p-x}) = p(\sqrt{p+x}-\sqrt{p-x})\]
- Expand the right-hand side: \[p \cdot \sqrt{p+x} - p \cdot \sqrt{p-x}\]
- Rearrange the terms: \[(\sqrt{p+x}+\sqrt{p-x}) - (p \cdot \sqrt{p+x} - p \cdot \sqrt{p-x}) = 0\]
- Combine like terms: \[(1-p)\sqrt{p+x} + (1+p)\sqrt{p-x} = 0\]
- Set the coefficients of the square roots to zero:
- [1-p] = 0 implies p = 1 (not possible since the denominator cannot be zero)
- Multiply both sides by: (1-p) \neq 0
- Square the equation: (1/p^2)(p+x) = (1/p^2)(p-x) which implies: (p+x) + (p-x) = 0\]
- Solve for x: \[(2p) = p\] \[x = \frac{2p^2}{p^2+1}\]
Thus, the correct answer is \[\frac{2p^2}{p^2+1}\], which is the option C.
Similar Questions
- If \(\frac{1}{a}+\frac{1}{b}=\frac{5}{6}\) and \(\frac{1}{a^2}+\frac{1}{b^2}=\frac{13}{36}\), then what is \(\frac{1}{a^3}+\frac{1}{b^3}\) equal to?
- If \(x^4 = x^2 + 1\), where \(x > 0\), then what is \(2x^4\) equal to?
- If \(x-\frac{1}{x}=2\), \(x > 0\); then what is \(x^2-\frac{1}{x^2}\) equal to?
- If \((a-b)^2 + (b - c)^2 + (c-a)^2 = 6\) and \(a^2 + b^2+c^2 = 29\), then what is \((a + b + c)\) equal to?
- If \(p=\frac{\sqrt{5}+2}{\sqrt{5}-2}\) and \(q=\frac{\sqrt{5}-2}{\sqrt{5}+2}\), then what is \(\frac{p}{q}+\frac{q}{p}\) equal to?
- If \(x=2+2^{1/2}+2^{3/2}\), then what is \(x^2-4x-10\) equal to?
Important Questions from Algebric Equations
A group of 630 children is seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?
The letters L, M, N, 0, P, Q, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3.
What is the integer assigned to N?
Four persons, Alok, Bhupesh, Chander and Dinesh have a total of Rs. 100 among themselves. Alok and Bhupesh between them have as much money as Chander and Dinesh between them, but Alok has more money than Bhupesh; and Chander has only half the money that Dinesh has. Alok has in fact Rs. 5 more than Dinesh has.
Who has the maximum amount of money?
If x=3/2, then the value of 27x3-54x2+36x-11 is
If a+b+c = 6 and ab+bc+ca = 11, then the value of bc(b+c) + ca(c+a) +ab(a+b) +3abc is
