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U = ( a^2 cos^2x + b^2 sin^2 x)^1/2 + (a^2 sin^2x + b^2 cos^2x)^1/2 then maximun and minimum of U^2

U = ( a^2 cos^2x + b^2 sin^2 x)^1/2 + (a^2 sin^2x + b^2 cos^2x)^1/2 then maximun and minimum of U^2
 

Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years ago
U^2= a^2+b^2+2*root(a^2*b^2+(a^2-b^2)^2sin^2(2x)/4)
but sin^22x lies between 0 and 1
so 2|ab|
or (|a|+|b|)^2
so, min and max value of U^2 are (|a|+|b|)^2 and 2*[a^2+b^2] respectively

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