Question

Помогите, плиз!
Заранее спасибо.

Answer 1

$1) (1+3 sqrt{5} ) ^{2} =1+45+6 sqrt{5} =46+6 sqrt{5} \ 2)(2 sqrt{3} -7) ^{2} =12+49-28 sqrt{2} = \ =61-28 sqrt{2} \ 3)(2 sqrt{10} - sqrt{2} ) ^{2} =40+4-4 sqrt{20} = \ =44-4*2 sqrt{5} =44-8 sqrt{5} \ \ 1) frac{ sqrt{x} -5}{25-x} =- frac{5- sqrt{x} }{25-x} =- frac{5- sqrt{x} }{(5- sqrt{x} )(5+ sqrt{x} )} = \ =- frac{1}{5+ sqrt{x} } \ \ 2) frac{ sqrt{2} +2}{ sqrt{2} } = frac{ sqrt{2} (1+ sqrt{2} )}{ sqrt{2} } =1+ sqrt{2}$


$3) frac{5+ sqrt{10} }{ sqrt{10} } = frac{ sqrt{5}( sqrt{5} + sqrt{2} ) }{ sqrt{10} } = frac{ sqrt{5} + sqrt{2} }{ sqrt{2} } \ \ 4) frac{2 sqrt{3}-3 }{5 sqrt{3} } = frac{ sqrt{3}(2- sqrt{3} )}{5 sqrt{3} } = frac{2- sqrt{3} }{5}$

Answer 2

1) (1+3√5)²=1²+2*1*3√5+(3√5)²=1+6√5+45=6√5+46
2)(2√3-7)²=(2√3)²-2*2√3*7+7²=12-28√3+49=61-28√3
3)(2√10-√2)²=(2√10)²-2*2√10*√2+(√2)²=40-4√20+2=42-4*2√5=42-8√5


1)$frac{ sqrt{x} -5}{25-x} =- frac{ sqrt{x} -5}{x-25} =- frac{ sqrt{x} -5}{( sqrt{x} )^{2} - 5^{2} } =- frac{ sqrt{x} -5}{( sqrt{x} - 5)( sqrt{x} + 5)} } =- frac{1}{ sqrt{x} +5}$
2)$frac{ sqrt{2}+2 }{ sqrt{2} }= frac{ sqrt{2}( sqrt{2}+2 )}{ sqrt{2}* sqrt{2} } frac{2+2 sqrt{2}}{2} = frac{2(1+ sqrt{2})}{2} =1+ sqrt{2}$
3)$frac{5+ sqrt{10} }{sqrt{10}} = frac{sqrt{10}(5+sqrt{10})}{sqrt{10}*sqrt{10}} = frac{5sqrt{10}+10}{10} = frac{5(sqrt{10}+2)}{10} = frac{sqrt{10}+2}{2}$
4)$frac{2 sqrt{3}-3 }{5sqrt{3}} = frac{sqrt{3}(2sqrt{3}-3)}{5sqrt{3}*sqrt{3}} = frac{6-3sqrt{3}}{5*3} = frac{3(2-sqrt{3})}{5*3} = frac{2-sqrt{3}}{5}$