Question

If (7a+8b)(7c-8d)=(7a-8b)(7c+8d) . prove that a:b=c:d​

Answer 1

Answer:

Yes you are right that a:b=c:d

Answer 2

Step-by-step explanation:

Now,

$\mathrm{(7a+8b)(7c-8d)=(7a-8b)(7c+8d)}$

$\Rightarrow \mathrm{\dfrac{7a+8b}{7a-8b}=\dfrac{7c+8d}{7c-8d}}$

Using Componendo - Dividendo method, we get

$\mathrm{\dfrac{(7a+8b)+(7a-8b)}{(7a+8b)-(7a-8b)}=\dfrac{(7c+8d)+(7c-8d)}{(7c+8d)-(7c-8d)}}$

$\Rightarrow \mathrm{\dfrac{7a+8b+7a-8b}{7a+8b-7a+8b}=\dfrac{7c+8d+7c-8d}{7c+8d-7c+8d}}$

$\Rightarrow \mathrm{\dfrac{14a}{16b}=\dfrac{14c}{16d}}$

$\Rightarrow \mathrm{\dfrac{a}{b}=\dfrac{c}{d}}$

$\Rightarrow \mathrm{a:b=c:d}$

Hence proved.