We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
48
1
avatar

Let \(x,y,z\) be real numbers such that \(\begin{align*} x + y + z &= 4, \\ x^2 + y^2 + z^2 &= 6. \end{align*}\)
Let \(m\) and \( M\) be the smallest and largest possible values of \(x,\)respectively. Find \(m+M\)

 Apr 27, 2019
 #1
avatar+22149 
+1

Let \(x,y,z\) be real numbers such that

\(\begin{align*} x + y + z &= 4, \\ x^2 + y^2 + z^2 &= 6. \end{align*}\)
Let \(m\) and \(M\) be the smallest and largest possible values of \(x\) respectively.

Find \(m+M\)

 

see: https://doubtnut.com/question-answer/if-x-y-z-are-real-such-that-x-y-z4x2-y2-z2-6-then-x-in-1-11-2-0-2-3-23-42-32-2232900

 

\(\begin{array}{|rcll|} \hline m+M &=& \dfrac{2}{3} + 2 \\\\ \mathbf{m+M} &\mathbf{=} & \mathbf{\dfrac{8}{3}} \\ \hline \end{array}\)

 

laugh

 Apr 29, 2019

9 Online Users