If a- b- c are non zero real numbers- then minimum value of the expressiona4 - a2 - 1b4 - 7b2 - 1c4 - 11c2 - 1-a2 b2c2 is

((a^4 + a^2 + 1)(b^4 + 7b^2 + 1)(c^4 + 11c^2 + 1)/(a^2 b^2c^2)) nbsp;= (a^2 + 1/a^2 + 1) + (b^2 + 1/b^2 + 7) + (c^2 + 1/c^2 + 11) Using A.M ≥ G.M we know tha ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Mathematics

AM,GM,HM Inequality

If a, b, c ar...

Question

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

315

No worries! We‘ve got your back. Try BYJU‘S free classes today!

351

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

415

No worries! We‘ve got your back. Try BYJU‘S free classes today!

451

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $351$
$(\frac{(a^{4} + a^{2} + 1) (b^{4} + 7 b^{2} + 1) (c^{4} + 11 c^{2} + 1)}{(a^{2} b^{2} c^{2})}) = (a^{2} + \frac{1}{a^{2}} + 1) + (b^{2} + \frac{1}{b^{2}} + 7) + (c^{2} + \frac{1}{c^{2}} + 11)$
Using $A . M \geq G . M$ we know that $x^{2} + \frac{1}{x^{2}} \geq 2$
The minimum value of the expression will occur when all the terms are mininum,
$= (2 + 1) (2 + 7) (2 + 11) = 351$

Suggest Corrections

Similar questions

Q. If

a, b, c

are non zero real numbers, then minimum value of the expression

(\frac{(a^{4} + a^{2} + 1) (b^{4} + 7 b^{2} + 1) (c^{4} + 11 c^{2} + 1)}{(a^{2} b^{2} c^{2})})

Q. If

a, b, c

are non zero real numbers, then minimum value of the expression

(\frac{(a^{4} + a^{2} + 1) (b^{4} + 7 b^{2} + 1) (c^{4} + 11 c^{2} + 1)}{(a^{2} b^{2} c^{2})})

Q. If

a, b, c

are non-zero real numbers then the minimum value of the expression

\frac{(a^{4} + a^{2} + 1) (b^{4} + 7 b^{2} + 1) (c^{4} + 11 c^{2} + 1)}{a^{2} b^{2} c^{2}}

equals :-

Q. If

a + b + c = 9

(where a, h, c are real numbers), then the minimum value of

a^{2} + b^{2} + c^{2}

Q. If

a_{1}, a_{2}, . . a_{n}

are positive real numbers whose product is a fixed number

c

, then the minimum value of

a_{1} + a_{2} +, . . a_{n - 1} + 2 a_{n}

Join BYJU'S Learning Program

If a,b,c are non zero real numbers, then minimum value of the expression((a4+a2+1)(b4+7b2+1)(c4+11c2+1)(a2b2c2)) is

The correct option is B 351((a4+a2+1)(b4+7b2+1)(c4+11c2+1)(a2b2c2))=(a2+1a2+1)+(b2+1b2+7)+(c2+1c2+11) Using A.M≥G.M we know that x2+1x2≥2 The minimum value of the expression will occur when all the terms are mininum, =(2+1)(2+7)(2+11)=351

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