Сумму квадратов находим как:
![x^2+px+q=0
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x_1^2+x_2^2=x_1^2+x_2^2+2x_1x_2-2x_1x_2=(x_1+x_2)^2-2x_1x_2=
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=(-p)^2-2q=p^2-2q](https://tex.z-dn.net/?f=x%5E2%2Bpx%2Bq%3D0%0A%5C%5C%5C%0Ax_1%5E2%2Bx_2%5E2%3Dx_1%5E2%2Bx_2%5E2%2B2x_1x_2-2x_1x_2%3D%28x_1%2Bx_2%29%5E2-2x_1x_2%3D%0A%5C%5C%5C%0A%3D%28-p%29%5E2-2q%3Dp%5E2-2q "x^2+px+q=0
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x_1^2+x_2^2=x_1^2+x_2^2+2x_1x_2-2x_1x_2=(x_1+x_2)^2-2x_1x_2=
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=(-p)^2-2q=p^2-2q")
0} \atop {x^2+ 5x + 3 = 0,x<0}} \right. \\\ \left \{ {{x_1= \frac{5+ \sqrt{13} }{2} ,x_2=\frac{5- \sqrt{13} }{2},x>0} \atop {x_3=\frac{-5+ \sqrt{13} }{2},x_4=\frac{-5- \sqrt{13} }{2},x<0}} \right. \\\
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x_1^2+x_2^2=(-5)^2-2\cdot3=19
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x_3^2+x_4^2=5^2-2\cdot3=19
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x_1^2+x_2^2+x_3^2+x_4^2=19+19=38" alt="x^2- 5|x| + 3 = 0 \\\ \left \{ {{x^2- 5x + 3 = 0,x>0} \atop {x^2+ 5x + 3 = 0,x<0}} \right. \\\ \left \{ {{x_1= \frac{5+ \sqrt{13} }{2} ,x_2=\frac{5- \sqrt{13} }{2},x>0} \atop {x_3=\frac{-5+ \sqrt{13} }{2},x_4=\frac{-5- \sqrt{13} }{2},x<0}} \right. \\\
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x_1^2+x_2^2=(-5)^2-2\cdot3=19
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x_3^2+x_4^2=5^2-2\cdot3=19
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x_1^2+x_2^2+x_3^2+x_4^2=19+19=38" align="absmiddle" class="latex-formula">
Ответ: 38