Question

If x=(7+21+ 35+49 ... +119), y = (4 + 12 + 20+ +44) and z = x - y₁ then root(3, 2z - 117) equals​

Answer 1

Given:

If x=(7+21+ 35+49+ ... +119), y = (4 + 12 + 20+... +44) and z = x - y₁

To Find:

Find the 3rd root of (2z-117)

Solution:

Before proceeding further let us know the basic formula of the sum of the odd numbers i.e

                                              $\sum(odd)=n^2$

where,

          n=the no of odd numbers

So, now calculating the value of x and y

$x=7+21+35+...+119\\=7(1+3+5+...+17)\\=7*n^2\\=7*9^2\\=7*81\\=567$

similarly calculating for y using the sum of odd numbers formula

$y=4+12+20+...+44\\=4(1+3+5+...+11)\\=4*6^2\\=4*36\\=144$

Now the value z is

$z=x-y\\=567-144\\=423$

Now finding the given value

$=\sqrt[3]{2z-117}\\=\sqrt[3]{2*423-117}\\=\sqrt[3]{846-117}\\=\sqrt[3]{729}\\=9$

Hence, the 3rd root of (2z-117) equals to 9.