Question

if (√3+√7)/(√7-√3)=a-b√21, find the value of a and b​

Answer 1

Answer:

(√3+√7)/(√7-√3) = a-b√21

here LHS = (√3+√7)/(√7-√3)

on rationalising multipling both numerator and denominator by (√7 + √3)

(√3+√7)(√7 + √3) / (√7-√3) (√7 + √3)

= (√3+√7)²/ (√7)²-(√3)²           [(a-b)(a+b) = a²-b² ]

= (√3+√7)²/ (7-3)

= {(√3)²+(√7)² + (2×√3×√7)} / 4     [ (a+b)² = a²+b²+2ab ]

=(3+7+ 2√21) / 4

=(10+2√21)/4

it is given that (√3+√7)/(√7-√3)=a-b√21

so  (10+2√21)/4 = a-b√21

10/4 + (2√21)/4 = a-b√21

   therefore a = 10/4 = 5/2

                    b = -2/4 = -1/2