If $a + b + c + d = 37$ ,

$b + c + d = 7$ ,

$a + c = 3$ ,

$bd - c^{2} = 29$ ,

Then find the value of $a^{2} +b^{2}+c^{2}+d^{2}$ .

The answer is 1269.

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$(a^2+b^2+c^2+d^2)= (a+b+c+d)^2-2(b+c+d)(a+c)-2(bd -c^2) = 37^2-2\cdot \cdot 3 -2\cdot 29 = 1269$