If a , b , c are non-zero real numbers then the minimum value of the expression (((a8+4 a4+1)(b4+3 b2+1)(c2+2 c+2)/a4 b2)) equals

Question

If a , b , c are non-zero real numbers then the minimum value of the expression (((a8+4 a4+1)(b4+3 b2+1)(c2+2 c+2)/a4 b2)) equals (A) 24 (B) 30 (C) 48 (D) 12

Tardigrade Admin · Accepted Answer

E=(a4+4+(1/a4))(b2+3+(1/b2))((c+1)2+1) E min =(6)(5)(1)=30

Q. If $a, b, c$ are non-zero real numbers then the minimum value of the expression $(\frac{( a ^{8} + 4 a ^{4} + 1 ) ( b ^{4} + 3 b ^{2} + 1 ) ( c ^{2} + 2 c + 2 )}{a ^{4} b ^{2}})$ equals

24

30

48

12

$E = (a^{4} + 4 + \frac{1}{a ^{4}}) (b^{2} + 3 + \frac{1}{b ^{2}}) ((c + 1)^{2} + 1)$
$E_{m i n} = (6) (5) (1) = 30$

Q. If a,b,c are non-zero real numbers then the minimum value of the expression (a4b2(a8+4a4+1)(b4+3b2+1)(c2+2c+2)​) equals

24

30

48

12

E=(a4+4+a41​)(b2+3+b21​)((c+1)2+1) Emin​=(6)(5)(1)=30

Q. If $a, b, c$ are non-zero real numbers then the minimum value of the expression $(\frac{( a ^{8} + 4 a ^{4} + 1 ) ( b ^{4} + 3 b ^{2} + 1 ) ( c ^{2} + 2 c + 2 )}{a ^{4} b ^{2}})$ equals

$E = (a^{4} + 4 + \frac{1}{a ^{4}}) (b^{2} + 3 + \frac{1}{b ^{2}}) ((c + 1)^{2} + 1)$
$E_{m i n} = (6) (5) (1) = 30$