Question

plzz answer with step by step explanation ​

Answer 1

Answer:

1/2 or 3/2

Step-by-step explanation:

Given equation is x²+x-2.

Comparing this equation with standard quadratic equation ax²+bx+c

so here a=1, b=1, c= -2.

as we know α+β = -b/a and α×β = c/a

Therefore putting value of a, b and c in above formulas

α+β= -1/1= -1 -------> eqn 1

β=-1-α = -(1+α)

and, α×β = -2/1 = -2 -------> eqn 2

Now, putting value of β in eqn 2

eqn 2 becomes

=> α×(-(1+α)) = -2

=> - (α+α²) = -2

=> α+α² = 2

=> α²+α-2=0

=> α² + 2α - α - 2 =0

=> α( α + 2) - (α + 2)=0

=> (α - 1)(α + 2) = 0

therefore α = 1 or -2

Case 1: taking  α =1

Putting value of α in eqn 1

1 + β = -1

β = -1 -1

β = -2

Now, solving (1/α-1/β)

taking lcm equation becomes

(β-α)/αβ ------>eqn 3

Now putting value of α = 1 and β = -2 in eqn 3

it becomes

(-2-1)/-2= -3/ -2

=> 3/2

Case 2: (Taking value of α = -2)

Putting α = -2 in eqn 1

-2 + β = -1

β = 1

putting values of α = -2 and β = 1 eqn 3 becomes

( 1 - (-2) ) / ( -2 ) = -1/-2

=> 1/2

Hence, the answer is 1/2 or 3/2