If a^2−b^2=2352 and a^2+b^2=5090 then what is the value of 29ab?

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30 Jan 2018 Find the Value

If a^2−b^2=2352 and a^2+b^2=5090 then what is the value of 29ab?

OPtion

1) 65253
2) 65353
3) 65463
4) 65653
5) 65453
6) 65853
7) 65353
8) 63253
9) 65293
10) None of these

Solution

As per question
a^2 - b^2 = 2352 ...(1)
a^2 + b^2 = 5090...(2)

Adding (1) and (2), we get
2a^2 = 7442
=> a^2 = 3721
=> a = 61

Subtracting (1) from (2), we get
2b^2 = 2738
=> b^2 = 1369
=> b = 37

29*a*b= 13*61*37 = 65453

Correct Option: 5 Best Solution (1)