Let A=[\table 1 , -1 ; 2 , \alpha] and B=[\table \beta , 1 ; 1 , 0], \alpha, \beta \in R. Let \alpha_1 be the value of \alpha which satisfies ( {\A}+ {\B})^2- {\A}^2+[\table 2 , 2 ; 2 , 2] and \alpha_2 be the value of \alpha which satisfies ( {\A}+ {\B})^2- {\B}^2. Then |\alpha_1-\alpha_2| is equal to _______. [28-Jul-2022-Shift-1]

JEE Mains 28-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 25 of 90

Marks: +1, -0

Let A=[

1	−1
2	α

] and B=[

β	1
1	0

],α,β∈R. Let α1 be the value of α which satisfies (A+B)2−A2+[

2	2
2	2

] and α2 be the value of α which satisfies (A+B)2−B2. Then |α1−α2| is equal to _______.

[28-Jul-2022-Shift-1]

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−1	−1−α
2+2α	α2−2

2β	α−β+1−1−α
α+2β+1+2+2α	α2−2+1

β−1	1
α+2β	2

β+2	α−β
1	−1

β2+1	β
β	1

β2+2β	α+1
α+3β+1	2