Question

if X square + Y square is equals to 6 x y prove that 2 log( x + Y)
is equal to log x + log Y + 3 log 2

Answer 1

⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐

-: EXPLANATION :-

✔ First we have to solve the given data to a relevant extent.

✔ Here, we had firstly find the value of (x+y). We replace it in the Left-Hand-Side term.

✔ We proceeded and our logarithmic equation is proved further.

❄❄❄❄ SOLUTION ❄❄❄❄

Given, x²+y² = 6xy
=> (x+y)²-2xy = 6xy
=> (x+y)² = 8xy
=> (x+y) = √8xy

Now,
L. H. S. = 2log(x+y)
= 2 log (√8xy)
= log (√8xy)²
= log 8xy
= log (2³× x × y)
= log x + log y + 3 log 2 = R. H. S.

Thus, L. H. S. = R. H. S. (Proved)

⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐