Question

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

Answer 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)

→ (√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

Answer 2

The value of a is 0 & b is -2/3