3^2x-6(3^x)-27=0
hi, i was prepping for my finals when i came along this question, i could not solve it, so could someone me and explain the answer. you.

2

Step-by-step explanation:

This is a quadratic in terms of .

I'm going to substitute :

This is actually factorable since all you have to do is find two numbers that multiply to be -27 and add to be -6.

These numbers are -9 and 3 since (-9)(3)=-27 while -9+3=-6.

This implies that either u-9=0 or u+3=0.

u-9=0 when u=9. (I added 9 on both sides here.)

u+3=0 when u=-3. (I subtracted 3 on both sides here.)

Recall the substitution:

So replacing our solutions that are in terms of u to in terms of x:

or

The second equation has no real solution. for all x.

So there is no way you find an x such that would be negative.

We only need to solve:

Check:

Replace x with 2 in given problem:

which is a true equation so x=2 checks out.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb