marienoel320
Answered

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. 



Answer :

konrad509
[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]
luana
[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]