Question:
The minimum value of x⁴+y⁴+z⁴xyz for positive real numbers x,y,z is
The minimum value of x⁴+y⁴+z⁴xyz for positive real numbers x,y,z is
Show Hint
Symmetric expressions attain extrema when variables are equal.
Updated On: Mar 18, 2026
- \sqrt2
- 2\sqrt2
- 4\sqrt2
- 8\sqrt2
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: By AM–GM inequality.
Step 2: Minimum occurs at x=y=z.
Step 3: Substituting gives 8\sqrt2.
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
- If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to
- $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to
- An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is
- $2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
View More Questions
Top BITSAT Algebra Questions
- Roots of the equation \( x^2 + bx - c = 0 \) (\( b, c>0 \)) are:
- If the arithmetic mean of two distinct positive real numbers \(a\) and \(b\) (where \(a>b\)) is twice their geometric mean, then \(a : b\) is:
- The coefficient of \(x^2\) term in the binomial expansion of \(\left(\frac{1}{3}x^{\frac{1}{3}} + x^{-\frac{1}{4}}\right)^{10}\) is:
- The coefficient of the highest power of \(x\) in the expansion of \((x + \sqrt{x^2 - 1})^8 + (x - \sqrt{x^2 - 1})^8\) is:
- If the 17th and the 18th terms in the expansion of \((2 + a)^{50}\) are equal, then the coefficient of \(x^{35}\) in the expansion of \((a + x)^{-2}\) is:
View More Questions
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions