Question

Late A1 A2 A3 A4 be real numbers such that A1 + 2 + 3 + 4 is equal to zero and a square A 1 square + 8 square + 3 square + a square is equal to 1 then the smallest possible give smallest value of the A1 - 82 whole square + 82 - 3 whole square + a 3 - 4 square + 4 - 4 - 1 whole square

Answer 1

I am not sure. But I will try to do it.

A1 + 2 + 3 + 4 = 0

A1 + 9 = 0

A1 = -9

A1² + 8² + 3² + a² = 1

(-9)² + 8² + 3² + a² = 1

81 + 64 + 9 + a² = 1

a² = 1 - 154 = -153

a = √-153 = (-153)¹/²

(A1 - 82)² + (82 - 3)² + (a³ - 4² + 4 - 4 - 1)²

(-9 - 82)² + (82 - 3)² + (-153³/²  - 4² - 1)²

(-91)² + (79)² + (-153³/² + 16 -1)²

8281 + 6241 + (-153³/² + 15)²

14522 + (-153)³ + 15² + (30 x -153³/²)

14522 - 3581577 + 225 + 30√-153³

3566830 + (30 x 153 x√-153)

3566830 + 4590√153