Question

(5√2-e)(3√2+e)= 1√2-6

Given that e and f are positive integers,
find the value of e and the value f

Answer 1

Hi,

e=6, f=12

Explanation:

`(5√(2)-e)( 3√(2) +e)=f√(2) -6\\\\30-3e√(2) -e^2+5e√(2) =f√(2) -6\\\\30+2e√(2) -e^2 =f√(2) -6\\\\`

`\left\{\begin{array}{ccc}30-e^2&=&-6\\2e&=&f\\\end{array} \right\\\\\\\left\{\begin{array}{ccc}e^2-36&=&0\\2e&=&f\\\end{array} \right\\\\\\\left\{\begin{array}{ccc}e&=&6\\f&=&12\\\end{array} \right\ or\ \left\{\begin{array}{ccc}e&=&-6\\f&=&-12\\\end{array} \right\\ e\ and\ f\ are\ positive\ integers\\\\\boxed{e=6\ and\ f=12}\\`