Question

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

Answer 1

Answer:

98

Step-by-step explanation:

Here,

a = 5 + 2√6

b = 1/a

= 1/( 5 + 2√6)

= (5 -2√6)/(5+2√6)(5 -2√6)

= (5 -2√6)/{5² -(2√6)²}

= (5 -2√6)/(25 -24)

= 5 -2√6

Now,

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

= 98

Hence, a² + b² = 98