Question

If 2/5x-2/1=-3/5+5,then the value of x is​

Answer 1

Answer:

Let roots of given equation be α and β

α.β=1

⇒β=  

α

1

​  

 

Hence α  

5

+(  

α

1

​  

)  

5

 is same as α  

5

+β  

5

 

Now

α  

2

−5α+1=0

β  

2

−5β+1=0

multiplying by α  

n−2

 and β  

n−2

 and reaarranging

α  

n

=5α  

n−1

−α  

n−2

 

β  

n

=5β  

n−1

−β  

n−2

 

Adding we get

α  

n

+β  

n

=5α  

n−1

+5β  

n−1

−α  

n−2

−β  

n−2

 

let α  

n

+β  

n

 be A  

n

​  

 

Then

A  

n

​  

=5A  

n−1

​  

−A  

n−2

​  

 

A  

0

​  

=2 and  

A  

1

​  

=5 sum of roots.

Hence  

A  

2

​  

=25−2=23

A  

3

​  

=115−5=110

A  

4

​  

=550−23=527

A  

5

​  

=2635−110=2525

Step-by-step explanation:

Answer 2

Step-by-step explanation:

2/5x-2/1=-3/5

x-2/1=3/5÷2/5

After cancellation

x-2=3/2

x=3/2+2

x=7/2

or

x=3.5