3 equations and 3 variables
Find the sum of all possible values of which satisfy the simultaneous equations , and , where and are reals.
The answer is 1.
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1 solution
⎩ ⎪ ⎨ ⎪ ⎧ x 2 − 4 y + 7 = 0 y 2 − 6 z + 1 4 = 0 z 2 − 2 x − 7 = 0 Adding the three equations, we have, x 2 − 4 y + 7 + y 2 − 6 z + 1 4 + z 2 − 2 x − 7 = 0 Rearranging the terms and completing the square, ( x − 1 ) 2 + ( y − 2 ) 2 + ( z − 3 ) 2 = 0 Hence x = 1 , y = 2 , z = 3 are the only solutions and can easily be verified.
Therefore, the sum of all possible values for x is 1