If a,b,and c are non-zero real numbers,then t | vedclass

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

Question

(B) The given expression is $\left(\frac{a^{4}+a^{2}+1}{a^{2}}\right)\left(\frac{b^{4}+7 b^{2}+1}{b^{2}}\right)\left(\frac{c^{4}+11 c^{2}+1}{c^{2}}\ri

Vedclass · Accepted Answer

$351$

Vedclass · Answer

(B) The given expression is $\left(\frac{a^{4}+a^{2}+1}{a^{2}}ight)\left(\frac{b^{4}+7 b^{2}+1}{b^{2}}ight)\left(\frac{c^{4}+11 c^{2}+1}{c^{2}}ight)$.This can be rewritten as $\left(a^{2}+\frac{1}{a^{2}}+1ight)\left(b^{2}+\frac{1}{b^{2}}+7ight)\left(c^{2}+\frac{1}{c^{2}}+11ight)$.Using the identity $x^2 + \frac{1}{x^2} = (x - \frac{1}{x})^2 + 2$,we get:$\left[(a-\frac{1}{a})^{2}+3ight]\left[(b-\frac{1}{b})^{2}+9ight]\left[(c-\frac{1}{c})^{2}+13ight]$.The minimum value of $(x - \frac{1}{x})^2$ is $0$,which occurs when $x^2 = 1$.Thus,the minimum value of the expression is $3 	imes 9 	imes 13 = 351$.

List-$I$	List-$II$
$(I) \ 3 \sin^2 x + 4 \cos^2 x - 2$	$(a) \ [\frac{1}{4}, 1]$
$(II) \ \cos^2 x + \sin^4 x$	$(b) \ [-\frac{1}{4}, \frac{1}{4}]$
$(III) \ \sin^6 x + \cos^6 x$	$(c) \ [1, 2]$
$(IV) \ \cos x \cos(\frac{2 \pi}{3} + x) \cos(\frac{2 \pi}{3} - x)$	$(d) \ [\frac{3}{4}, 1]$
	$(e) \ [0, 1]$

If $a$,$b$,and $c$ are non-zero real numbers,then the minimum value of the expression $\left( \frac{(a^4 + a^2 + 1)(b^4 + 7b^2 + 1)(c^4 + 11c^2 + 1)}{a^2 b^2 c^2} \right)$ is

Similar Questions

The maximum value of the function $y = e^{5 + \sqrt{3} \sin x + \cos x}$ is

The minimum value of $8 \cos^2 x + 18 \sec^2 x$ for all $x \in R$ wherever it is defined,is:

The minimum value of the function $f(x) = |\sin x + \cos x + \tan x + \cot x + \sec x + \csc x|$ is equal to

The maximum value of the expression $\frac{1}{\sin^2 \theta + 3 \sin \theta \cos \theta + 5 \cos^2 \theta}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module