if a+1/a=6 and a is not equal to 0 then find a-1/a

Question

It is from class 9 text book. Pls help

Answer 1

me assume that stuf shood be

(a+1)/a=6

or a+1=6a

so 5a=1

or a=1/5 or 0.2

Me assume yu want part 2...(a-1)/a

become...-0.8/0.2...=-8/2...=-4

Answer 2

a + 1/a = 6 (a≠0) ··· Eq.1   

Multiply both sides of Eq.1 by a, then put the equation into the standard form of quadratic.   We have:

a²－6a + 1 = 0   Solve the equqtion for a, using the quadratic formula.   We have:

a=(6 ± √(6²－4·1·1)) / 2·1 = 3 ± 2√2   We have: a=3+2√2, or a=3－2√2

From Eq.1, 1/a=6－a

A. If a=3+2√2, 1/a=6－(3+2√2)=3－2√2, so a－1/a=(3+2√2)－(3－2√2)=4√2  

B. If a=3－2√2, 1/a=6－(3－2√2)=3+2√2, so a－1/a=(3－2√2)－(3+2√2)=－4√2

From A. and B., We have: a－1/a=±4√2 

The answer is: If a=3+2√2, a－1/a=4√2, or if a=3－2√2 , a－1/a=－4√2