Question

Find the value of <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $a$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $b^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $c^3$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $d^4$.
Given that $a$, $b$, $c$ and $d$ are the x co-ordinates of the points which are reflections of (4, 3), (3, 2), (2, 1) and (1, 0) in x-axis.

Answer 1

Let us name the points first.
M (4, 3)
N (3, 2)
O (2, 1)
P (1, 0).

Now, reflections of these points in x-axis can be written as:
M' (4, -3)
N' (3, -2)
O' (2, -1)
P' (1, 0)

Therefore, according to the question:
$a$ = 4, $b$ = 3, $c$ = 2, and $d$ = 1

Hence,
$a$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $b^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $c^3$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $d^4$ = 4 + 9 + 8 + 1 = 22.