Question

if a² + b² = 14ab then show that a + b / 4 = ½ (log a + log b)​

Answer 1

Answer:

Hence proved in the above picture.

Answer 2

Given:

a² + b² = 14ab

To prove:

a + b / 4 = ½ (log a + log b)​

Solution:

Given

a² + b² = 14ab

We will use this equation and proceed step by step to reach the conclusion.

a² + b² - 14ab  = 0

Adding and subtracting 2ab

a² + b² + 2ab - 2ab - 14 ab = 0

(a + b)² - 16ab = 0              { a² + b² + 2ab = (a + b)²}

(a + b)² = 16ab

Taking square root both side

a + b = 4√ab

(a + b) / 4 = √ab

If we take log on the R.H.S we have

(a + b) / 4 = log($(ab)^{1/2}$)

a + b / 4 = ½ (log a + log b)​

Hence, proved