Question

If x2+y2 =14xy prove that 2log (x+y)=4log 2+log x+log y

Answer 1

x^2 + y^2 = 14xy

x^2 + y^2 + 2xy = 14xy + 2xy

(x+y)^2 = 16 xy

Taking log on both sides

log(x+y)^2 = log(16 xy)

2 log(x+y) = log 16 + log x + log y

2log(x+y) = 4 log 2 + log x + log y.

Hence Proved.

Answer 2

Step-by-step explanation:

x² + y² =14xy

Adding 2xy on both sides

x² + y² +2xy = 14xy + 2xy

(x + y)² = 16xy

Applying log on both sides

log (x + y)² = log (16xy)

2 log x + y = log (4²xy)

2 log (x + y) = log 4² + log x + log y

.'. Hence Proved.

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