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If 33x - y = 81 and 3x + y = 729, find the product of x and y ,where x and y are two real numbers.


1. 6
2. 8
3. 8.75
4. 5.25

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Correct Answer - Option 3 : 8.75

Given

33x - y = 81

3x + y = 729

Formula/ Concept used

If am + n = ap then m + n = p

where m, n and p are real numbers.

Calculation

33x - y = 34

3x-y = 4      ......(1)

3x + y = (32)3

x + y = 6      ......(2)

on adding equation (1) and (2)

4x = 10

x = 2.5

put x= 5 in equation (2)

y = 6 - x

y = 6 - 2.5 = 3.5

∴ x × y = 2.5 × 3.5 = 8.75

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