Question

Find the value of a and b if 5 + √6 / 5 - √6 = a + b √6

Answer 1

5+√6/5-√6×5+√6/5+√6
31+10√6/19
a=31/19
b√6=10√6/19
b=10/19

Answer 2

Q. 5-✓6/5+✓6=a-b✓6 find a and b

Solution:-

=> 5-√6/5+√6=a-b√6

=> (5-√6)/(5+√6)= (a) - (b√6)

Take Conjugate pair of (5+√6).

=>(5-√6)/(5+√6) × (5-√6)/(5-√6)

= (a) - (b√6)

we know that (a+b) (a-b) = (a)²-(b)²

=> (5-√6)²/( (5)² - (√6)² )= (a) - (b√6)

=> ((5)² - 2×5√6 +(√6)² )/(25 - 6)

= (a) - (b√6)

=> (25 - 10√6 + 6 )/(19)= (a) - (b√6)

=> (25 + 6 - 10√6 )/(19)= (a) - (b√6)

=> (31 - 10√6 )/(19) = (a) - (b√6)

=> (31/19) - ( (10/19)×√6 )= (a) - (b√6)

so, by conclusion or comparing.

=> a = (31/19) and b = (10 /19)

i hope it helps you.