If a^2 x^4 + b^2 y^4 = c^6,then the maximum v | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation $a^2 x^4 + b^2 y^4 = c^6$. Applying the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality for the two terms $a^2 x^4$ an

Vedclass · Accepted Answer

$\frac{c^3}{\sqrt{2ab}}$

Vedclass · Answer

(B) Given the equation $a^2 x^4 + b^2 y^4 = c^6$. Applying the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality for the two terms $a^2 x^4$ and $b^2 y^4$: $\frac{a^2 x^4 + b^2 y^4}{2} \geq \sqrt{(a^2 x^4)(b^2 y^4)}$ Substituting the given value $a^2 x^4 + b^2 y^4 = c^6$: $\frac{c^6}{2} \geq \sqrt{a^2 b^2 x^4 y^4}$ $\frac{c^6}{2} \geq ab x^2 y^2$ $x^2 y^2 \leq \frac{c^6}{2ab}$ Taking the square root on both sides: $xy \leq \frac{c^3}{\sqrt{2ab}}$ Thus,the maximum value of $xy$ is $\frac{c^3}{\sqrt{2ab}}$.

If $a^2 x^4 + b^2 y^4 = c^6$,then the maximum value of $xy$ is:

Similar Questions

The slant height of a right circular cone is $3 \text{ cm}$. The height of the cone for maximum volume is

If the function $f(x) = \begin{cases} \tan^{-1}x; & x < 1 \\ \sec^{-1}x + \lambda; & x \ge 1 \end{cases}$ has a local minimum at $x = 1$,then the range of $\lambda$ 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 . . . . . . .

The maximum area of a right-angled triangle with hypotenuse $h$ is

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module