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Online Quiz (Worksheet A B C D)

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High School Mathematics
3.14 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.

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