If 3x² + 2y² - 2z² - 9x + 2y + 8 = 0
2x² - y² + 5z² + 4x - 8y + 12z - 3 = 0
and 6z² - 4x² + 3y² - x + 2y + 9 = 0.
Then the value of 5x + 4y - 3z is (x, y, z are real numbers) =
Answers
Given : 3x² + 2y² - 2z² - 9x + 2y + 8 = 0
2x² - y² + 5z² + 4x - 8y + 12z - 3 = 0
and 6z² - 4x² + 3y² - x + 2y + 9 = 0.
To Find : value of 5x + 4y - 3z
Solution:
3x² + 2y² - 2z² - 9x + 2y + 8 = 0
2x² - y² + 5z² + 4x - 8y + 12z - 3 = 0
6z² - 4x² + 3y² - x + 2y + 9 = 0.
Add all 3
=> x² + 4y² +9z² -6x -4y + 12z + 14 = 0
=> x² -6x + 4y² - 4y + 9z² + 12z + 14 = 0
=> (x - 3)² - 9 + (2y - 1)² -1 + (3z + 2)² - 4 + 14 = 0
=> (x - 3)² + (2y - 1)² + (3z + 2)² - 14 + 14 = 0
=> (x - 3)² + (2y - 1)² + (3z + 2)² = 0
=> x = 3 , 2y = 1 3z = -2
=> 5x = 15 , 4y = 2 , -3z = 2
5x + 4y - 3z = 15 + 2 + 2
= 19
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