Question

# Form a quadratic equation whose roots are the numbers ( frac{1}{10-sqrt{72}} ) and ( frac{1}{10+6 sqrt{2}} )

Solution

The quadreatic equation is

[

begin{array}{l}x^{2}-left(frac{1}{10-sqrt{72}}+frac{1}{10+6 sqrt{2}}right) x+frac{1}{(10-sqrt{72})(10+6 sqrt{2})}=0 Rightarrow x^{2}-left(frac{1}{10-6 sqrt{2}}+frac{1}{10+6 sqrt{2}}right) x+frac{1}{(10-6 sqrt{2})(10+6 sqrt{2})}=0 Rightarrow x^{2}-left(frac{10+6 sqrt{2}+10-6 sqrt{2}}{100-72}right) x+frac{1}{100-72}=0 Rightarrow x^{2}-left(frac{20}{28}right) x+frac{1}{28}=0 Rightarrow 28 x^{2}-20 x+1=0end{array}

]