SSC CGL 2014 Tier 1 27 April shift 7

Question 113

If a = 2 + √3 ,then the value of $$(a^{2}+\frac{1}{a^{2}})$$ is

Solution

a = 2 + √3

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

here ,

$$a = 2+\sqrt{3}$$

$$\dfrac{1}{a} = \dfrac{1}{2+\sqrt{3}} \times\dfrac{2-\sqrt{3}}{2-\sqrt{3}} = 2-\sqrt{3}$$

$$a+\dfrac{1}{a} = 2+\sqrt{3} +  2-\sqrt{3}$$

$$a + \dfrac{1}{a} = 4$$

So, $$(a + \frac{1}{a})^2$$ - 2 = 14


Create a FREE account and get:

  • Free SSC Study Material - 18000 Questions
  • 230+ SSC previous papers with solutions PDF
  • 100+ SSC Online Tests for Free

cracku

Boost your Prep!

Download App