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### High School Mathematics3.14 Prove the Statements

 Example: If x2 + y2 = 7xy, prove that, 2log(x+y) = log x + log y + 2log 3. Solution: x2 + y2 = 7x Adding 2xy on both sides, we get, x2 + y2 + 2xy = 7xy + 2xy. (x + y)2 = 9xy (x + y)2 = 32 . x . y Taking logarithm on both sides, we get, log (x + y)2 = log (32 . x . y) 2 log (x + y) = log x + log y + 2 log 3. Directions: Prove the following statement. Also write at least ten examples of your own. 1. If x2 + y2 = 10xy, prove that, 2log(x + y) = log x + log y + 2log 2 + log 3. 2. If x2 + y2 = 15xy, prove that, 2log(x + y) = log x + log y + log 17. 3. If x2 + y2 = 8xy, prove that, 2log(x + y) = log x + log y + log 2 + log 5. 4. If x2 + y2 = 8xy, prove that, 2log(x - y) = log x + log y + log 2 + log 3. 5. If x2 + y2 = 10xy, prove that, 2log(x - y) = log x + log y + 3log 2. 6. If x2 + y2 = 18xy, prove that, 2log(x - y) = log x + log y + 4log 2.