Dividi il segmento ab lungo 99cm in tre parti, tali che la seconda abbia lunghezza doppia della prima la terza tripla della seconda.

Three parts are given by 11 cm, 22 cm and 66 cm.

Step-by-step explanation:

We are given a line segment AB of length 99 cm.

It is required to cut the line segment into three parts.

Let the first part be of length 'x' cm.

As, the second part is twice the length of the first part.

We get,

Length of the second part is '2x' cm.

Further, the third part is triple the second part.

This gives,

Length of the third part is '3(2x)' i.e. '6x' cm.

Since, the sum of all three parts is 99 cm.

So, x + 2x + 6x = 99

i.e. 9x = 99

i.e. x = 11 cm.

Then, 2x = 2 × 11 = 22 cm and 6x = 6 × 11 = 66 cm

Hence, the three parts are given by 11 cm, 22 cm and 66 cm.

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