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 ...

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Byju's Answer

Standard XII

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

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351

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415

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451

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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,
$= (2 + 1) (2 + 7) (2 + 11) = 351$

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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