Find the value of \(x + \frac{1}{x}\) if \(\sqrt{x} + \frac{1}{\sqrt{x}} = 3\).
7
Square both sides of the given equation \(\sqrt{x} + \frac{1}{\sqrt{x}} = 3\): \(\left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)^2 = 9\).
Expand: \(x + 2 \cdot \sqrt{x} \cdot \frac{1}{\sqrt{x}} + \frac{1}{x} = 9\) → \(x + 2 + \frac{1}{x} = 9\).
Therefore \(x + \frac{1}{x} = 9 - 2 = 7\).
Hence, the answer is 7.
Similar Questions
(x + 3)² is equal to:
Two rectangular fields have lengths \(x\) and \(y\) meters respectively, where \(x > y\). The sum of their lengths is equal to three times the difference of their lengths. What is the value of \(\dfrac{3xy}{2(x^{2} - y^{2})}\)?
Simplify: (a + b)² − (a − b)²
If x = 3, what is the value of the expression x2 + 2x + 1?
Simplify: (3a + 2b)2 + (3a − 2b)2 − 2(9a2 + 4b2)
Simplify the following expression.
\((2x + 3y)^{2} - (2x - 3y)^{2} + 12xy\)
To a square plot having an area of \(x\;\mathrm{m}^{2}\), a strip having an area of \(\dfrac{1}{4}\sqrt{x}\;\mathrm{m}^{2}\) and a patch having an area of \(a^{2}\;\mathrm{m}^{2}\) are added. If the total area can now be expressed as a perfect square using powers of \(x\) and constants, find the positive value of \(a\).
Simplify: \(\left(\frac{17a^{5}b^{2}c^{4}}{51a^{3}b^{3}c^{4}}\right)\times 9b^{3}\)
If \(a+b+c=6\), \(abc=-60\) and \(a^3+b^3+c^3=162\), find the value of \(ab+bc+ca\).
Which of the following equations represent the statement, \"one fifth of m is twice of one third of n\"?
Important Questions from Algebra
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
