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Question

Find the compound ratio of:

$$(a+b)^{2}:(a-b)^{2}$$

$$\left(a^{2}-b^{2}\right):\left(a^{2}+b^{2}\right)$$

$$\left(a^{4}-b^{4}\right):(a+b)^{4}$$


Solution

$$(a+b)^{2}:(a-b)^{2}$$

$$\left(a^{2}-b^{2}\right):\left(a^{2}+b^{2}\right)$$

$$\left(a^{4}-b^{4}\right):(a+b)^{4}$$

We can write it as

$$=\dfrac{(a+b)^{2}}{(a-b)^{2}}\times \dfrac{a^{2}-b^{2}}{a^{2}+b^{2}} \times \dfrac{a^{4}-b^{4}}{(a+b)^{4}}$$

By further calculation

$$=\dfrac{(a+b)^{2}}{(a-b)^{2}}\times \dfrac{(a+b)(a-b)}{a^{2}+b^{2}} \times \dfrac{\left(a^{2}+b^{2}\right)(a+b)(a-b)}{(a+b)^{4}}$$

So we get

$$=\dfrac{1}{1}$$

$$=1: 1$$


Mathematics

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