If (a−b)^2= 5ab, then log(a+b)/3 =
Answers
Answer
1/2 log a + 1/2 log b
Step-by-step explanation:
Given :
( a - b )² = 5 ab
By the laws of expansion we know that :
( a + b )² = a² + b² + 2 ab
Hence : ( a - b )² = a² + b² - 2 ab
⇒ ( a² + b² - 2 ab ) = 5 ab
Add 4 ab both sides :-
⇒ ( a² + b² + 2 ab ) = 5 ab + 4 ab
⇒ ( a + b )² = 9 ab
Take square root both sides :
⇒ a + b = 3√ab
Hence :
log ( a + b )/3
⇒ log ( 3√ab )/3
⇒ log √ab
⇒ 1/2 log ab
⇒ 1/2 ( log a + log b )
⇒ 1/2 log a + 1/2 log b
ANSWER:--------
( a + b )² = a² + b² + 2 ab
Hence : ( a - b )² = a² + b² - 2 ab
⇒ ( a² + b² - 2 ab ) = 5 abAdd 4 ab both sides :-
⇒ ( a² + b² + 2 ab ) = 5 ab + 4 ab
⇒ ( a + b )² = 9 abTake square root both sides :
⇒ a + b = 3√abHence :log ( a + b )/3
⇒ log ( 3√ab )/3
⇒ log √ab
⇒ 1/2 log ab
⇒ 1/2 ( log a + log b )⇒ 1/2 log a + 1/2 log
hence proved,
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