x,y,z are real numbers such that(x+y)(x+y+z)=120,(y+z)((x+y+z)=96,(x+z)(x+y+z)=72.what is the maximum value of |x+y+z|-z?
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Explanation:
(x+y+z)
2
=x
2
+y
2
+z
2
+2(xy+yz+zx)
⇒25=x
2
+y
2
+z
2
+6
⇒x
2
=19−(y
2
+z
2
)
As (y
2
+z
2
)≥0
⇒x
max
=19
⇒
x
max
=
19
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