Question

If √7−1/√7+1-√7+1/√7−1=a+b√7. Find a and b where a and b are rational numbers.

Answer 1

Answer:

-2$\sqrt{7}$/3

Step-by-step explanation:

[($\sqrt{7}$ -1/$\sqrt{7}$ +1)($\sqrt{7}$ -1/$\sqrt{7}$ -1)] - [($\sqrt{7}$ +1/$\sqrt{7}$ -1)($\sqrt{7}$ +1/$\sqrt{7}$ +1)]

[7 +1 -2$\sqrt{7}$/7-1] -[7+1 +2$\sqrt{7}$/7-1 ]

[7 +1 -2$\sqrt{7}$/6] -[7+1 +2$\sqrt{7}$/6 ]

[(8 -2$\sqrt{7}$) -(8 +2$\sqrt{7}$)]/6

[(8 -2$\sqrt{7}$-8 -2$\sqrt{7}$)]/6

[(8 -8 -2$\sqrt{7}$- 2$\sqrt{7}$)]/6

-4$\sqrt{7}$/6

-2$\sqrt{7}$/3