Question

a-1/a=12 then a square-1/a square =?​

Answer 1

Answer:

You forgot to mention options in the question. anyways .

Recalling the formulae ,

(a+b)2=(a−b)2+4ab  

Using the above formulae in the given question,

(a+1/a)2=(a−1/a)2+4a.(1/a)  

=(a−1/a)2+4  

Now,  (a−1/a)2+4−2(a−1/a)=12  

Let (a−1/a)=z.  

=z2−2z+4−12=0  

=z2−2z−8=0  

= z2−(4−2)z−8=0  

=  z2−4z+2z−8=0  

= z(z−4)+2(z−4)=0  

= (z−4)(z+2)=0  

Either z=4orz=−2  

Either a−1/a=4ora−1/a=−2  

Taking first expression ,  

=a−1/a=4  

= (a2−1)/a=4  

=a2−4a−1=0  

Solving the above quadratic we get

Either  a=(4+√(42−4.1.(−1))/2  

a=2+√5  

Or ,a=(4−√(42−4.1(−1))/2  

a=2−√5  

From second expression,

=(a−1/a)=−2  

=( a2−1)/a=−2  

= a2−1=−2a  

=a2+2a−1=0  

Solving the above quadratic we get,

=a=(−2+√(4−4.1.(−1))/2  

=a=−1+√2  

= a=(−2−√(4−4.1.(−1))/2  

a=−1−√2  

So the values of a are (2−√5),(2+√5) , (−1+√2), and (−1−√2) respectively

HOPE IT HELPS MARK AS BRAILIEST PLZ!!