Four Basic Operations In A System Of Equations
⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ x 1 + x 2 + x 3 + x 4 = 2 0 1 5 x 1 − x 2 − x 3 − x 4 = 2 × 2 0 1 5 x 1 × x 2 × x 3 × x 4 = 3 × 2 0 1 5 x 1 ÷ x 2 ÷ x 3 ÷ x 4 = 4 × 2 0 1 5
Find the number of ordered quadruples ( x 1 , x 2 , x 3 , x 4 ) of real numbers which satisfy the system of equations above.
The answer is 0.
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Very nice and surprisingly quick!
Adding the first two equations gives 2 x 1 = 3 ∗ 2 0 1 5 , and multiplying the last two gives x 1 2 = 1 2 ∗ 2 0 1 5 2 ... incompatible!