At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
[tex]2m^2-7m-3=0\\a=2;\ b=-7;\ c=-3\\\Delta=b^2-4ac\to\Delta=(-7)^2-4\cdot2\cdot(-3)=49+24=73\\\\x=\frac{-b\pm\sqrt\Delta}{2a}\to \boxed{x=\frac{7\pm\sqrt{73}}{2\cdot2}=\frac{7\pm\sqrt{73}}{4}}[/tex]
[tex]4b^2+8b+7=4\\4b^2+8b+7-4=0\\4b^2+8b+3=0\\4b^2+2b+6b+3=0\\2b(2b+1)+3(2b+1)=0\\(2b+1)(2b+3)=0\iff2b+1=0\ or\ 2b+3=0\\2b=-1\ or\ 2b=-3\\\boxed{b=-\frac{1}{2}\ or\ b=-\frac{3}{2}}[/tex]
[tex]5\sqrt{80a^2}=5\sqrt{80}\cdot\sqrt{a^2}=5\sqrt{16\cdot5}\cdot|a|=5\cdot\sqrt{16}\cdot\sqrt5\cdot|a|\\\\=5\cdot4\cdot\sqrt5\cdot|a|=\boxed{20|a|\sqrt5}[/tex]
[tex]-6\sqrt{150r}=-6\sqrt{25\cdot6r}=-6\sqrt{25}\cdot\sqrt{6r}=-6\cdot5\sqrt{6r}=\boxed{-30\sqrt{6r}}[/tex]
[tex]\frac{2}{\sqrt3}=\frac{2}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\boxed{\frac{2\sqrt3}{3}}[/tex]
[tex]\frac{\sqrt6}{5\sqrt3}=\frac{1}{5}\cdot\frac{\sqrt6}{\sqrt3}=\frac{1}{5}\sqrt\frac{6}{3}=\frac{1}{5}\sqrt2=\boxed{\frac{\sqrt2}{5}}[/tex]
[tex]4b^2+8b+7=4\\4b^2+8b+7-4=0\\4b^2+8b+3=0\\4b^2+2b+6b+3=0\\2b(2b+1)+3(2b+1)=0\\(2b+1)(2b+3)=0\iff2b+1=0\ or\ 2b+3=0\\2b=-1\ or\ 2b=-3\\\boxed{b=-\frac{1}{2}\ or\ b=-\frac{3}{2}}[/tex]
[tex]5\sqrt{80a^2}=5\sqrt{80}\cdot\sqrt{a^2}=5\sqrt{16\cdot5}\cdot|a|=5\cdot\sqrt{16}\cdot\sqrt5\cdot|a|\\\\=5\cdot4\cdot\sqrt5\cdot|a|=\boxed{20|a|\sqrt5}[/tex]
[tex]-6\sqrt{150r}=-6\sqrt{25\cdot6r}=-6\sqrt{25}\cdot\sqrt{6r}=-6\cdot5\sqrt{6r}=\boxed{-30\sqrt{6r}}[/tex]
[tex]\frac{2}{\sqrt3}=\frac{2}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\boxed{\frac{2\sqrt3}{3}}[/tex]
[tex]\frac{\sqrt6}{5\sqrt3}=\frac{1}{5}\cdot\frac{\sqrt6}{\sqrt3}=\frac{1}{5}\sqrt\frac{6}{3}=\frac{1}{5}\sqrt2=\boxed{\frac{\sqrt2}{5}}[/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
