Question

If a²+1/a²=66, then find the value of a-1/a (where a is greater than 1)​

Answer 1

Answer:

a²+1/a² = 66

Now,

(a-1/a)² = a²+1/a² -2(a)(1/a)

(a-1/a)² = a²+1/a² -2

(a-1/a)² = 66-2

(a-1/a)² = 64

a-1/a = root of 64

a-1/a = 8

Hope it helps!!

Have a great Day!!

Answer 2

Answer:

Step-by-step explanation:

• $a^{2}$+ 1/$a^{2}$ = 66  
• $(a+1/a)^{2}$ - 2*a*1/a = 66
• $(a+1/a)^{2}$= 68 ---------- 1

We know that $(a-b)^{2}$ = $(a+b)^{2}$ - 4ab

Here a= a , b = 1/a

$(a-1/a)^{2}$= $(a+1/a)^{2}$ - 4*a*1/a

$(a-1/a)^{2}$= 68 - 4 ( from 1 )

$(a-1/a)^{2}$= 64

a- 1/a = 8

Hope this answer helps you.