PROVE THAT:
=(9+ )^3+(9- )^3
2. =36 why?
The first one's giving me a headache, so I'll waffle at the second.
By definition, the "taking the logarithm of" function and the "raising e to the power of" are direct inverses.
That is, by definition, , if (it's undefined otherwise).
So we have (doing the same thing to both sides of the first of the above).
Then we note that from the second of the above, and so it follows directly that:
That holds for all and so definitely holds for .
Did you try just doing the arithmetic on the right?
So
so the terms involving cancel and the sum is 1728.
And, of course,
You could also have seen this by observing that the odd powers of will cancel while the even powers add:
[tex]= 2(9)(96)= 2(3^2)(4)(24)= 2(3^2)(4)(4)(2)(3)= (2^6)(3^3)= (4^3)(3^3)= ((4)(3))^2= (12)^3