[tex]\mathbf{ a).\: x=3\sqrt{5} +4}[/tex]
[tex]\mathbf{y=3\sqrt{5} -4}[/tex] [tex]\mathbf{ m_a=\dfrac{x+y}{2}=\dfrac{3\sqrt{5} +4+3\sqrt{5}-4 }{2} =\dfrac{3\sqrt{5} +3\sqrt{5} }{2} =\dfrac{6\sqrt{5} }{2}^{(2} =} \:\boxed{\mathbf{3\sqrt{5} }}[/tex]
[tex]\mathbf{ m_g=\sqrt{x\cdot y}=\sqrt{(3\sqrt{5}+4)\cdot (3\sqrt{5}-4) }=\sqrt{(3\sqrt{5})^2-4^2 } =\sqrt{9\cdot 5-16} = }\,\: \boxed{\mathbf{\sqrt{29} }}[/tex]
[tex]\mathbf{b).\: x=\sqrt{35} +4\sqrt{2} }[/tex]
[tex]\mathbf{y=\sqrt{35} -4\sqrt{2} }[/tex]
[tex]\mathbf{ m_a=\dfrac{x+y}{2}=\dfrac{\sqrt{35}+4\sqrt{2}+\sqrt{35}-4\sqrt{2} }{2} =\dfrac{\sqrt{35}+\sqrt{35} }{2} =\dfrac{2\sqrt{35} }{2}^{(2}}= \boxed{\mathbf{\sqrt{35}}}[/tex]
[tex]\mathbf{ m_g=\sqrt{x\cdot y}=\sqrt{(\sqrt{35}+4\sqrt{2})\cdot (\sqrt{35}-4\sqrt{2} ) } =\sqrt{\sqrt{35} ^2-(4\sqrt{2})^2} =\sqrt{35-16 \cdot 2 }=\boxed{\mathbf{\sqrt{3}}}}[/tex]
[tex]\mathbf{a).\: 4x+7x=11x}[/tex]
[tex]\mathbf{b). \: 5x-9x=-4x}[/tex]
[tex]\mathbf{c). \: 3x^2 + 6x-5+2x^2-9x-4=5x^2+6x-5-9x-4=5x^2-3x-5-4=5x^2-3x-9}[/tex]
[tex]\mathbf{d). \: 2(x+3)+5(x-2)=2x+6+5x-10=7x+6-10=7x-4}[/tex]
[tex]\mathbf{e). \: x(x+5)-2(1-x)=x^2+5x-2+2x=x^2+7x-2}[/tex]
[tex]\mathbf{f). \: (x+4)(x+2)=x\cdot x + 2x +4x+4 \cdot 2 = x^2+2x+4x+8=x^2+6x+8}[/tex]
[tex]\mathbf{g). \: (x-3)(x+5)=x\cdot x + 5x-3x-3 \cdot 5 = x^2 + 5x-3x-15=x^2+2x-15}[/tex]
[tex]\mathbf { h). \: (2x+1)(x-4)-(x+2)(3x+1)=2x^2-8x+x-4-(3x^2+7x+2)=-x^2-14x-6}[/tex]
