Solve q7 please Thanks a lot?

2x² −4x+5 =0
When α,β are the roots
The α+β =−(−4)/2=2 and
αβ=5/2=2.5

Equation whose roots are α+1/α and β+1/β is
x²−{(α+1/α) +( β+1/β)}x+(α+1/α)( β+1/β)=0
Now
{(α+1/α) +( β+1/β)} ={(α+ β)+(1/α+1/β)}
={(α+ β)+(α+ β)/αβ)} =2+2/(5/2=2+4/5=14/5
And
(α+1/α)( β+1/β) =(αβ+α/ β+β/α+1/αβ)=
={αβ+(α²+β²)/αβ+1/αβ}
Now (α²+β²)= (α+β)² −2αβ
=(2)² −2×5/2=4−5=−1
Hence
={αβ+(α²+β²)/αβ+1/αβ} ={5/2+(−1)/(5/2)+1/(5/2)}
={5/2−2/5+2/5}=5/2
Hence
The required equation x²−{(α+1/α) +( β+1/β)}x+(α+1/α)( β+1/β)=0 becomes
x²−{14/5}x+(5/2)=0
→10x²−28x+25=0

The equation is 10x^2-28x+25=0.

α +ß = 2 ; α ß = 5/ 2...[ x - a ] [ x - b ] = x² + ( - a - b ) + ab

[ x - ( α + 1 / α ) ] [ x - ( ß + 1 / ß )....here α & ß are conjugate complex...- 1 ± i √1.5

Use the quadratic formula.