Question

how was this problem solved?​

Answer 1

Solution:-

Given,

$\alpha = \frac{6 + \sqrt{4 \times 5} }{2}$

We know that √4 = 2

So,it becomes

$\alpha = \frac{6 + ( \sqrt{4} \times \sqrt{5} ) }{2}$

$\alpha = \frac{6 + 2 \sqrt{5} }{2}$

We can write 6 as 2 × 3

$\alpha = \frac{2 \times 3 + 2 \sqrt{5} }{2}$

Take two in common

$\alpha = \frac{2(3 + \sqrt{5}) }{2}$

Two in both numerator and denominator cancells

So, it becomes

$\alpha = 3 + \sqrt{5}$

Hope you understood!!