Question

Докажите тождество.....

Answer 1

$1) frac{37}{7+2sqrt3}+frac{37}{7-2sqrt3}= frac{37(7-2sqrt3)+37(7+sqrt3)}{7^2-(2sqrt3)^2} = frac{259-74sqrt2+259+74sqrt2}{49-4*3} =\= frac{518}{37} =14\ \ 2) frac{sqrt{10}+3}{sqrt{10}-3}+frac{sqrt{10}-3}{sqrt{10}+3}= frac{(sqrt{10}+3)(sqrt{10}+3)+(sqrt{10}-3)(sqrt{10}-3)}{(sqrt{10}-3)(sqrt{10}+3)}= \=frac{(sqrt{10}+3)^2+(sqrt{10}-3)^2}{sqrt{10}^2-9} = frac{10+6sqrt{10}+9+10-6sqrt{10}+9}{10-9}=38$

Answer 2

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