If a^2−b^2=2640 and a^2+b^2=6338 then what is the value of 23ab?

M4maths Previous Puzzles

02 Jan 2018 Find the Value

If a^2−b^2=2640 and a^2+b^2=6338 then what is the value of 23ab?

OPtion

1) 32491
2) 64013
3) 66263
4) 63097
5) 63079
6) 28813
7) 28816
8) 32491
9) 60263
10) None of these

Solution

As per question
a^2 - b^2 = 2640 ...(1)
a^2 + b^2 = 6338...(2)

Adding (1) and (2), we get
2a^2 = 8978
=> a^2 = 4489
=> a = 67

Substracting (1) from (2), we get
2b^2 = 3698
=> b^2 = 1849
=> b = 43

23*a*b= 23*67*43 = 66263

Correct Option: 3 Best Solution (7)