UPSC CDS 1 2022 Math Paper

Given:
43x×47y=(2021)2,x≠0,y≠0
To find ‌

4xy+x+y

2xy−x−y

Calculation:
We have 43x×47y=(2021)2
On factorization of 2021 we get
2021=43×47
So, we can write the equation (i) as
43x×47y=(43×47)2
⇒43x×47y=432×472
On comparing we get
x=2‌ and ‌y=2
Now we have to find the value of ‌

4xy+x+y

2xy−x−y

⇒‌

4×2×2+2+2

2×2×2−2−2

=‌

20

4

=5
∴ The required value is 5 .