Find the values forx, y, and z so that all the following statements are true.

x = -36, y = 6, z = -6

Step-by-step explanation:

The requirement x/z = -z means x = -z².

The requirement x/y = z means x = yz.

These two requirements together mean yz = -z², or y = -z.

The requirements that z/2 and z/3 are integers mean that z is a multiple of 2·3 = 6. The smallest magnitude non-zero multiple is z=-6 (since we also require z < -z).

Using z=-6, we have x = -z² = -36; y = -(-6) = 6.

For some positive integer n, ...

... x = -36n², y = 6n, z = -6n.

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

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.