Question

if a=5+2✓6 and b=1/a, what will be the value of a²+b²​

Answer 1

Given that :

a = 5 + 2√6.. (1)

b = 1/a.. (2)

Putting the value of a in eq. (2)

Rationalizing the denominator,

=1/( 5 + 2√6)

=> (5 - 2√6)/(5 + 2√6)(5 - 2√6)

=> (5 - 2√6)/[(5)² - (2√6)²]

=> (5 - 2√6)/(25 - 24)

=> 5 - 2√6

Now,

To find : a²+b²

We know that,

a² + b² = (a + b)² - 2ab

=> (5 + 2√6 + 5 - 2√6)² - 2(5 + 2√6)(5 - 2√6)

=(10)² - 2 × (25 -24)

=100 - 2 × 1

= 98

Thus, Value of a² + b² = 98.

Answer 2

Answer:

Given that:

$\tt{b = \frac{1}{a}}$

=》 $\tt{b = \frac{1}{5 + 2\sqrt{6}}}$

Rationalise it :

=》 $\tt{b = \frac{1}{5 +2\sqrt{6}} \times \frac{5-2\sqrt{6}}{5-2\sqrt{6}}}$

=》 $\tt{5 - 2\sqrt{6}}$

Now, $\tt{a^{2} + b^{2}}$ will be:

$\tt{(5+2\sqrt{6})^{2} + (5-2\sqrt{6})}$

=》 $\tt{25+24+20\sqrt{6} +25+24-20\sqrt{6}}$

=》 $\tt{98}$