
Example: If x^{2} + y^{2} = 7xy, prove that, 2log(x+y) = log x + log y + 2log 3. Solution: x^{2} + y^{2} = 7x Adding 2xy on both sides, we get, x^{2} + y^{2} + 2xy = 7xy + 2xy. (x + y)^{2} = 9xy (x + y)^{2} = 3^{2} . x . y Taking logarithm on both sides, we get, log (x + y)^{2} = log (3^{2} . 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 x^{2} + y^{2} = 10xy, prove that,
2. If x^{2} + y^{2} = 15xy, prove that,
3. If x^{2} + y^{2} = 8xy, prove that,
4. If x^{2} + y^{2} = 8xy, prove that,
5. If x^{2} + y^{2} = 10xy, prove that,
6. If x^{2} + y^{2} = 18xy, prove that, 