Question

A.The sum of a whole number and its reciprocal is$\frac{10}{3}$ . Can you guess the number.

B.Seven times the reciprocal of a number added to$\frac{2}{3}$ gives $3$ . what is that number ?

Answer 1

$A.$ $x+\frac{1}{x}=\frac{10}{3}\therefore x^2+1=\frac{10x}{3}\Rightarrow 3x^2+3=10x\Rightarrow 3x^2-10x+3=0\Rightarrow 3x^2-x-9x-3=0\Rightarrow x(3x-1)-3(3x-1)=0\Rightarrow (3x-1)(x-3)=0$

Either ,

$3x-1=0x=\frac{1}{3}$

or ,

$x-3=0x=3\therefore x=\frac{1}{3}$

Or , $x=3.$

$B.$ Let the no: be $x$

$\frac{7}{x}+\frac{2}{3}=3\Rightarrow 21+2x=9x\Rightarrow -7x=-21\Rightarrow x=3\because \frac{7}{x}+\frac{2}{3}=3\therefore \frac{7}{3}+\frac{2}{3}=3$

$\therefore$ The no: is $3.$