Question:
The number of solutions of the equation
\[
9\sqrt{x} - 9\sqrt{x} + 2 = 2x - 7\sqrt{x} + 3 = 0
\]
is:
The number of solutions of the equation
\[
9\sqrt{x} - 9\sqrt{x} + 2 = 2x - 7\sqrt{x} + 3 = 0
\]
is:
Show Hint
When dealing with square roots in equations, try substitution to simplify the expression and reduce it to a quadratic form.
Updated On: Mar 24, 2025
- 3
- 1
- 2
- 4
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
- First, express the equation in a simpler form using substitution, such as \( y = \sqrt{x} \), transforming the equation into a quadratic form.
- Solve the quadratic equation to find the number of real solutions for \( x \).
- The number of solutions is 2.
Was this answer helpful?
0
0
Top Questions on Algebra
- Let \( f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) \) be a polynomial of degree 2, satisfying \( f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) \). If \( f(K) = -2K \), then the sum of squares of all possible values of \( K \) is:
If the set of all values of \( a \), for which the equation \( 5x^3 - 15x - a = 0 \) has three distinct real roots, is the interval \( (\alpha, \beta) \), then \( \beta - 2\alpha \) is equal to
If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to .
- Let \( f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) \) be a polynomial of degree 2, satisfying \( f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) \). If \( f(K) = -2K \), then the sum of squares of all possible values of \( K \) is:
- In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
- \(R\) and \(S\) scored the same on the first test.
- From the second test onwards, \(R\) consistently scored the same (a non-zero score).
- The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
- From the fifth test onwards, \(S\) scored the same as \(R\).
- The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
View More Questions
Questions Asked in JEE Main exam
- The product B formed in the following reaction sequence is: \[ {C}_6{H}_5{CN} \xrightarrow{{HCl}} (A) \xrightarrow{{AgCN}} (B) \]
- JEE Main - 2025
- Organic Chemistry
- What are the units of viscosity, intensity of wave, and pressure gradient?
- JEE Main - 2025
- Units and measurement
- If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to:
- JEE Main - 2025
- Matrices and Determinants
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- The distance of the point \( P(1, 2, 3) \) from the plane \( 3x - 4y + 12z - 7 = 0 \) is:
- JEE Main - 2025
- Geometry and Vectors
View More Questions