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CBSE Class 11-science Answered

x,y,z belong to R x+y+z=4 ,x^2+y^2+z^2=6 ,find maximum possible value of z.
Asked by aahnik.mohanty | 21 Jun, 2019, 09:09: PM
answered-by-expert Expert Answer
x plus y plus z equals 4 rightwards double arrow x plus y equals 4 minus z A l s o comma space x squared plus y squared plus z squared equals 6 rightwards double arrow space x squared plus y squared equals 6 minus z squared N o w comma 2 x y equals open parentheses x plus y close parentheses squared minus open parentheses x squared plus y squared close parentheses equals open parentheses 4 minus z close parentheses squared minus open parentheses 6 minus z squared close parentheses equals 16 plus z squared minus 8 z minus 6 plus z squared equals 2 z squared minus 8 z plus 10 T h e space q u a d r a t i c space e q space w i t h space r o o t s space x space a n d space y space i s u squared minus open parentheses x plus y close parentheses u plus x y equals 0 u squared minus open parentheses 4 minus z close parentheses u plus 2 z squared minus 8 z plus 10 equals 0 S i n c e comma space x comma space y greater or equal than 0 rightwards double arrow D greater or equal than 0 open parentheses 4 minus z close parentheses squared minus 4 open parentheses 2 z squared minus 8 z plus 10 close parentheses greater or equal than 0 rightwards double arrow 16 plus z squared minus 8 z minus 8 z squared plus 32 z minus 40 greater or equal than 0 rightwards double arrow 3 z squared minus 8 z plus 4 less or equal than 0 rightwards double arrow z element of open square brackets 2 over 3 comma 2 close square brackets
Answered by Renu Varma | 24 Jun, 2019, 12:05: PM

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