По теореме Виета:
[tex] {x}^{2} + bx + c = 0 \\ x_{1} + x _{2} = - b \\ x_{1} \times x _{2} = c[/tex]
[tex] {x}^{2} - 16x + 9 = 0 \\x_{1} + x _{2} = - ( - 16) = 16 \\ x_{1} \times x _{2} =9 \\ \\ 15 \sqrt{ x_{1} x _{2} } - ( x_{1} + x _{2}) {}^{2} = \\ 15 \sqrt{9} - {16 {}^{} }^{2} =45 - 256 = - 211[/tex]
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По теореме Виета:
[tex] {x}^{2} + bx + c = 0 \\ x_{1} + x _{2} = - b \\ x_{1} \times x _{2} = c[/tex]
[tex] {x}^{2} - 16x + 9 = 0 \\x_{1} + x _{2} = - ( - 16) = 16 \\ x_{1} \times x _{2} =9 \\ \\ 15 \sqrt{ x_{1} x _{2} } - ( x_{1} + x _{2}) {}^{2} = \\ 15 \sqrt{9} - {16 {}^{} }^{2} =45 - 256 = - 211[/tex]