Question

FOR THE BRAINLEIST USERS:

Solve the 25 sum

I will mark U as a Brainleist

Answer 1

$\textbf{Hey there}$!


$\textbf{Solution}$:


Taking L.H.S:


= $\begin{vmatrix}x + y +2 z&x&y \\ \\ z&2x + y + z&y\\ \\ z&x&x + 2y + z \end{vmatrix}$


Applying $C_{1}$ ➡ $C_{1}$ + $C_{2}$ + $C_{3}$


= $\begin{vmatrix}2(x + y + z)&x&y \\ \\ 2(x + y + z)&2x + y + z&y\\ \\ 2(x + y + z)&x&x + 2y + z \end{vmatrix}$


Taking 2 ( x + y + z ) common from $C_{1}$


=2(x+ y+z)$\begin{vmatrix} 1&x&y \\ \\ 1 &2x + y + z &y\\ \\ z&x&x + 2y + z \end{vmatrix}$


Applying $R_{1}$ ➡ $R_{1}$ - $R_{2}$


=2(x+ y+z) $\begin{vmatrix} 0& - x - y - z&0 \\ \\ 1 &2x + y + z &y\\ \\ 1&x&x + 2y + z \end{vmatrix}$


Expanding by $R_{1}$


= 2 ( x + y + z ) [ - ( -x - y - z )( x + 2y + z - y )]


= 2 ( x + y + z ) [( x + y + z ) ( x + y + z )]


= 2 ( x + y + z ) $(x + y + z) ^{2}$


= 2 $( x + y + z )^{3}$


Hence Proved.



#Be Brainly.

Answer 2

!

:

Taking L.H.S:

=

Applying  ➡  +  +

=

Taking 2 ( x + y + z ) common from

=2(x+ y+z)

Applying  ➡  -

=2(x+ y+z)

Expanding by

= 2 ( x + y + z ) [ - ( -x - y - z )( x + 2y + z - y )]

= 2 ( x + y + z ) [( x + y + z ) ( x + y + z )]

= 2 ( x + y + z )

= 2

Hence Proved.