Question

The minimum value of 27^cosx + 81^sinx is –

• A. $\frac { 1 } { 3 \sqrt { 3 } }$
• B. $\frac { 2 } { 3 \sqrt { 3 } }$
• C. $\frac { 1 } { 9 \sqrt { 3 } }$
• D. ) $\frac { 2 } { 9 \sqrt { 3 } }$

Answer 1

Answer: (B)

$\frac { 2 } { 3 \sqrt { 3 } }$

Answer 2

27^cosx and 81^sinx are positive no. and for positive no.

AM ³ GM

Ž 27^cosx + 81^sinx ³ 2. (27^cosx.81^sinx)^1/2

³ 2.(3^{3cosx + 4sinx})^1/2

³ 2.(3^–5)^1/2

³ $\frac { 2 } { 9 \sqrt { 3 } }$