The master mind's problem
⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ X 2 + 3 Y 2 + X Y = 2 5 , 3 Y 2 + Z 2 = 9 , Z 2 + Z X + X 2 = 1 6 If X , Y and Z are positive real numbers satisfying the system of equations above, find X Y + 2 Y Z + 3 Z X .
The answer is 41.6.
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Form a right angled with sides3,4 and 5 from given information as the equations given are like cosine rule and pythagoras theorem.Find area of the triangle which is the required answer:24√3.