If x, y, z and w are non-zero real numbers and x2 +5y2+
5z2 + 4w -4xy - 4yz - 4zw = 0 then x, y, z are in
Answers
Given : x, y, z and w are non-zero real numbers
x² + 5y² + 5z² + 4w² - 4xy - 4yz - 4zw = 0
To find : x, y, z and w are in
GP , AP , HP , none
Solution:
x² + 5y² + 5z² + 4w² - 4xy - 4yz - 4zw = 0
=> x² + 4y² + y²+ 4z² + z² + 4w² - 4xy - 4yz - 4zw = 0
=> x² + 4y² - 4xy + y²+ 4z² - 4yz + z² + 4w² - 4zw = 0
=> (x - 2y)² + (y - 2z)² + (z - 2w)² = 0
As square can not be negative and sum is zero
Hence each square term must be zero
(x - 2y)² = 0
(y - 2z)² =0
(z - 2w)² = 0
=> x = 2y , y = 2z , z = 2w
x , y , z w are in GP
x/y = 2 = y/z = z/w
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Answer:
Step-by-step explanation: