if (m+n)P2 = 90 and (m-n)P2 = 30 then find m and n

Dear student
We have,Pm+n,2=90 and Pm-n,2=30Consider,Pm+n,2=90m+n!m+n-2!=90m+nm+n-1m+n-2!(m+n-2)!=90m+nm+n-1=90Since 10×10-1=90So, m+n=10    ....(1)Consider,Pm-n,2=30m-n!(m-n-2)!=30m-nm-n-1m-n-2!m-n-2!=30m-nm-n-1=30Since 6×6-1=30So, m-n=6     ...(2)Solving (1) and (2), we get m=8 and n=2
Regards

  • 6
m=60 and n=30
  • -7
What are you looking for?