Question

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 1

`Reciprocal \ of\ a \ number\ x:\\ (1)/(x)\\ \\7+(1)/(x)=2x\ |*x\\ 7x+1=2x^2\\ -2x^2+7x+1=0\\\\ \Delta=7^2-4*(-2)*1=49+8=57\\ √(\Delta)=√(57)\\ x_1=(-7-√(57))/(-4)\\ or\ x_2=(-7+√(57))/(-4)`

Answer 2

`(1)/(x)+7=2x\\ 1+7x=2x^2\\ 2x^2-7x-1=0\\ \Delta=(-7)^2-4\cdot2\cdot(-1)=49+8=57\\ √(\Delta)=√(57)\\ x_1=(-(-7)-√(57))/(2\cdot2)=(7-√(57))/(4)\\ x_2=(-(-7)+√(57))/(2\cdot2)=(7+√(57))/(4)\\`