Question

Aratati ca Numarul a=
$(\sqrt{27} + 2 \sqrt{2} )( \sqrt{35 - 12 \sqrt{6} } ) + (5 \sqrt{2} - 7)(5 \sqrt{2} + 7)$
este numar natural. plssss​

Answer 1

(5√2-7)(5√2+7)=(5√2)²-7²=25*2-49=50-49=1

12√6=√864

√(35-√864)=√[(35+√(35²-864))/2]-√[(35-√(35²-864))/2]=√[(35+√(1225-864))/2]-√[(35+√(1225-864))/2]=√[(35+√361)/2]-√[(35-√361)/2]=√[(35+19)/2]-√[(35-19)/2]=√(54/2)-√(16/2)=√27-√8=√27-2√2

(√27+2√2)(√(35-√864)=(√27+2√2)(√27-2√2)=√27²-(2√2)²=27-4*2=27-8=19

(√27+2√2)(√(35-√864)+(5√2-7)(5√2+7)=19+1=20∈N