Question

If 4a2 +9b2 +16c2 –6ab –12bc –8ca =0, prove that 2a=3b=4c

Answer 1

Step-by-step explanation:

Given If 4a2 +9b2 +16c2 –6ab –12bc –8ca =0, prove that 2a=3b=4c

• Now we have the equation and we need to prove that 2a = 3b = 4c
• Equation is 4a^2 + 9b^2 + 16 c^2 – 6ab – 12bc – 8ca = 0
• We can write this as
•                 4a^2 + 9b^2 + 16c^2 – (2a)(3b) – (3b)(4c) – (3b)(4c) – (4c)(2a) = 0  
• So we get
• (2a – 3b)^2 + (3b – 4c)^2 + (4c – 2a)^2 = 0
• So equating each term to 0 we get
• 2a = 3b = 4c