IDNLearn.com is designed to help you find reliable answers quickly and easily. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

seven more than the reciprocal of a number is equal to twice the number. If X is the number, write an equation that can be used to find the number. 

Sagot :

[tex]\frac{1}{x}+7=2x\\ 1+7x=2x^2\\ 2x^2-7x-1=0\\ \Delta=(-7)^2-4\cdot2\cdot(-1)=49+8=57\\ \sqrt{\Delta}=\sqrt{57}\\ x_1=\frac{-(-7)-\sqrt{57}}{2\cdot2}=\frac{7-\sqrt{57}}{4}\\ x_2=\frac{-(-7)+\sqrt{57}}{2\cdot2}=\frac{7+\sqrt{57}}{4}\\ [/tex]
[tex]Reciprocal \ of\ a \ number\ x:\\ \frac{1}{x}\\ \\7+\frac{1}{x}=2x\ |*x\\ 7x+1=2x^2\\ -2x^2+7x+1=0\\\\ \Delta=7^2-4*(-2)*1=49+8=57\\ \sqrt{\Delta}=\sqrt{57}\\ x_1=\frac{-7-\sqrt{57}}{-4}\\ or\ x_2=\frac{-7+\sqrt{57}}{-4}[/tex]