Question

If log (x-y/4) log √x + log √y then show
that (x+y)² = 20 xy.​

Answer 1

(x + y)² = 20xy  if log ((x - y)/4)  = log√x + log√y

Step-by-step explanation:

log ((x - y)/4)  = log√x + log√y

log a + log b = log (ab)

=> log ((x - y)/4)  = log√xy

=> (x - y)/4 = √xy

=> (x - y) = 4√xy

Squaring both sides

=> x² + y² - 2xy = 16xy

=> x² + y² = 18xy

adding 2xy both sides

=> x² + y² + 2xy = 18xy + 2xy

=> (x + y)² = 20xy

QED

Proved

(x + y)² = 20xy  if log ((x - y)/4)  = log√x + log√y

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