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Question
If log`( a - b )/2 = 1/2( log a + log b )`, Show that : a2 + b2 = 6ab.
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Solution
log`(( a - b )/2)= 1/2( log a + log b )`
⇒ log`(( a - b )/2) = 1/2( log ab ) `
⇒ log`(( a - b )/2) = log (ab)^(1/2)`
⇒ `(( a - b )/2) = (ab)^(1/2)`
Squaring both sides we have,
`(( a - b)/2)^2 = ab`
⇒ `( a - b )^2/4 = ab`
⇒ ( a - b )2 = 4ab
⇒ a2 + b2 - 2ab = 4ab
⇒ a2 + b2 = 4ab + 2ab
⇒ a2 + b2 = 6ab.
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