Question

Find the value of a and b
√ 7-1/√ 7+1-√ 7+1/√ 7-1=a+b√ 7

Answer 1

Explanation:

Hi friend!!

√7-1/√7+1 – √7+1/√7-1

→ (√7-1)/(√7+1) × (√7-1)/(√7-1) – (√7+1)/(√7-1) × (√7+1)/(√7+1)

→ (√7-1)²/(√7+1)(√7-1) – (√7+1)²/(√7-1)(√7+1)

→ {√7²+1²-2(√7)(1)}/(√7²-1²) – {√7²+1²+2(√7)(1)}/(√7²-1²)

→ (7+1-2√7)/6 – (7+1+2√7)/6

→ (8-2√7)/6 – (8+2√7)/6

→ {8-2√7-8-2√7}/6

→ -4√7/6

→ 0+(-2/3)√7 = a+√7b

Therefore, a = 0 and b = -⅔

Hope it helps.

Answer 2

a=
`(2)/(3)`,b=
`-(2)/(3)`

Explanation:

Original=
`((√(7) -1)^(2) )/(7-1) -((√(7) +1)^(2) )/(7-1)`

=
`((√(7) -1)-(√(7) +1)^(2) )/(6)`

=
`((√(7)-1+√(7) -1)(√(7) -1 -√(7) -1))/(6)`

=
`(-4√(7) +4)/(6)`

=
`(2)/(3) -(2)/(3) √(7)`

Contrast factor

a+b√ 7=
`(2)/(3) -(2)/(3) √(7)`

and so a=
`(2)/(3)`,b=
`-(2)/(3)`