$$\frac{(415+223)^{2}+(415-223)^{2}}{(415\times415+223\times223)}=?$$

Solution

Expression : $$\frac{(415+223)^{2}+(415-223)^{2}}{(415\times415+223\times223)}=?$$

Let $$415 = a$$ and $$223 = b$$

=> $$x = \frac{(a + b)^2 + (a - b)^2}{a^2 + b^2}$$

= $$\frac{(a^2 + b^2 + 2ab) + (a^2 + b^2 - 2ab)}{a^2 + b^2}$$

= $$\frac{2a^2 + 2b^2}{a^2 + b^2}$$

= $$\frac{2 (a^2 + b^2)}{a^2 + b^2} = 2$$

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