Question 117

If $$x^{2}+\frac{1}{5}x+a^{2}$$ is a perfect square then a is

Solution

Expression : $$x^{2}+\frac{1}{5}x+a^{2}$$

= $$[(x^2) + (2 * \frac{1}{10} * x) + (\frac{1}{10})^2] + a^2 - (\frac{1}{10})^2$$

= $$(x + \frac{1}{10})^2 + a^2 - (\frac{1}{10})^2$$

Now, for the above expression to be perfect square,

=> $$a^2 - (\frac{1}{10})^2 = 0$$

=> $$a^2 = (\frac{1}{10})^2$$

=> $$a = \frac{1}{10}$$

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