NDA2019MathematicsApplication of DerivativesActual
What is the minimum value of a^2 ^2 x + b^2 ^2 x where a 0 and b 0 ?
Options
- A(a+b)^2
- B(a-b)^2
- Ca^2+b^2
- D|a^2+b^2 |
Correct answer
A. (a+b)^2
Step-by-step solution
For minimum value aligned & a^2 ^2 x + b^2 ^2 x & =a^2 ^2 x+b^2 cosec ^2 x & =a^2 (1+ ^2 x )+b^2 (1+ ^2 x ) & =a^2+b^2+Q^2 ^2 x+b^2 ^2 x & a^2 ^2 x+b^2 ^2 x 2 a b & minimum value =a^2+b^2+2 a b & =(a+b)^2 aligned