Question

If a=√8-√7 and a=1/b, then a²+b²-3ab/a²+ab+b²=?​

Answer 1

Answer:

(a²+b²-3ab)/(a²+ab+b²)=(267-60√14)/221

Step-by-step explanation:

given,

a=√8-√7, a=1/b

or, b=1/a

=1/(√8-√7)

or, b=√8+√7

now,

a²+b²-3ab=8+2√56+7+8-2√56+7-3√56=30-6√14

again,

a²+ab+b²=8+2√56+7+√56+8-2√56+7=30+2√14

than,

(a²+b²-3ab)/(a²+ab+b²)=(15-3√14)/(15+√14)=(15-3√14)(15-√14)/225-14)=(225-15√14-45√14+42)/211=(267-60√14)/221