4a^2+9b^2+16c^2+1/9a^2+1/16b^2+25c^2=133/30. ;1440a^2b^2c^2=
Answers
1440a²b²c² = 1 if 4a² + 9b² + 16c² + 1/9a² + 1/16b² + 1/25c² = 133/30
Step-by-step explanation:
4a² + 9b² + 16c² + 1/9a² + 1/16b² + 1/25c² = 133/30
=> (2a)² + (1/3a)² + (3b)² + (1/4b)² + (4c)² + (1/5c)² = 133/30
=> (2a - 1/3a)² + 2(2a)(1/3a) + (3b - 1/4b)² + 2(3b)(1/4b) + (4c - 1/5c)² + 2(4c)(1/5c) = 133/30
=> (2a - 1/3a)² + 4/3 + (3b - 1/4b)² + 3/2 + (4c - 1/5c)² + 8/5 = 133/30
=> (2a - 1/3a)² + 40/30 + (3b - 1/4b)² + 45/30 + (4c - 1/5c)² + 48/30 = 133/30
=> (2a - 1/3a)² + (3b - 1/4b)² + (4c - 1/5c)² + 133/30 = 133/30
=> (2a - 1/3a)² + (3b - 1/4b)² + (4c - 1/5c)² = 0
=> (2a - 1/3a)² = 0 => 2a - 1/3a = 0 => 6a² = 1
(3b - 1/4b)² = 0 => 3b - 1/4b = 0 => 12b² = 1
(4c - 1/5c)² = 0 => 4c - 1/5c = 0 => 20c² = 1
(6a²)( 12b²)(20c²) = 1 * 1 * 1
=> 1440a²b²c² = 1
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