Question 96

If $$a : b = 2 : 5$$, then $$a^2 - ab + b^2 : a^2 + ab + b^2 =$$

Solution

Given, a : b = 2 : 5

Let a = 2k and b = 5k

$$a^2-ab+b^2=\left(2k\right)^2-\left(2k\right)\left(5k\right)+\left(5k\right)^2=4k^2-10k^2+25k^2=19k^2$$

$$a^2+ab+b^2=\left(2k\right)^2+\left(2k\right)\left(5k\right)+\left(5k\right)^2=4k^2+10k^2+25k^2=39k^2$$

$$\therefore\ $$ $$a^2 - ab + b^2 : a^2 + ab + b^2 = 19k^2 : 39k^2 = 19 : 39$$

Hence, the correct answer is Option A

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