Question

15. If a = 5 + √24 and ab = 1, what is the value of
a- ab + b2?​

Answer 1

Answer:

Firstly, ab = 1 => b = 1/a => b² = 1/a²

√ 24 = √(2² * 2 * 3) = 2√6

a - ab + b² = 5 + √24 - 1 + 1/(5+√24)²

= 4 + 2√6 + 1/(25 + 100√6 + 24)

= 4 + 2√6 + 1/(49+100√6)

=

$\frac{1849 + 498 \sqrt{6} }{49 + 100 \sqrt{6} }$

This is approximately equal to 10.44006......