Find the value of x, if:

Solution:

(i) Let us consider the following equation:

$4 x=(52)^{2}-(48)^{2}$

Using the identity $(a+b)(a-b)=a^{2}-b^{2}$, we get:

$4 x=(52)^{2}-(48)^{2}$

$4 x=(52+48)(52-48)$

$4 x=100 \times 4=400$

$\Rightarrow 4 x=400$

$\Rightarrow x=100$        (Dividing both sides by 4)

(ii) Let us consider the following equation:

$14 x=(47)^{2}-(33)^{2}$

Using the identity $(a+b)(a-b)=a^{2}-b^{2}$, we get:

$14 x=(47)^{2}-(33)^{2}$

$14 x=(47+33)(47-33)$

$14 x=80 \times 14=1120$

$\Rightarrow 14 x=1120$

$\Rightarrow x=80$             (Dividing both sides by 14)

(iii) Let us consider the following equation:

$5 x=(50)^{2}-(40)^{2}$

Using the identity $(a+b)(a-b)=a^{2}-b^{2}$, we get:

$5 x=(50)^{2}-(40)^{2}$

$5 x=(50+40)(50-40)$

$5 x=90 \times 10=900$

$\Rightarrow 5 x=900$

$\Rightarrow x=180$    (Dividing both sides by 5)