Find the value of x, if:
(i) 4x = (52)2 − (48)2
(ii) 14x = (47)2 − (33)2
(iii) 5x = (50)2 − (40)2
(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)
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