Question

$\sqrt{14 + 6 \sqrt{5} } = a + \sqrt{b \:} \: then \: find \: b {?}^{2} - a {?}^{2}$
This is the question, please answer with the whole solution... ​

Answer 1

Answer:

-4

Step-by-step explanation:

Given :

√14 + 6√5

=> √9 + 5 + 6√5 = a + √b

=> √3² + (√5)² + 2 * 3√5 = a + √b

[∵ a² + b² + 2ab = (a + b)²]

=> √(3 + √5)² = a + √b

=> 3 + √5 = a + √b

Thus,

a = 3, b = √5

Then,

b² - a² = (√5)² - (3)²

          = 5 - 9

         = -4

Hope it helps!