Simplify 4\2-root 2 + 5 \root 2-1

asked Sep 24, 2021 143k views

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5 votes

Answer:

Explanation:

Use FOIL method

$(√(2) -1)(2-√(2))= √(2)*2 -√(2)*√(2) -1*2-1*(-√(2))\\\\\\=2√(2) - 2 -2 +√(2)$

Combine like terms

$=2√(2) +√(2) - 2 -2\\\\\\=(2+1)√(2) - 4\\\\\\=3√(2)-4$

$(4)/(2-√(2))+(5)/(√(2) -1)=(4*(√(2) -1))/((2-√(2))*(√(2) -1))+(5*(2-√(2)))/((√(2) -1)(2-√(2)))\\\\\\=(4√(2)-4+10-5√(2))/((√(2) -1)(2-√(2)))$

$=(4√(2)-5√(2)-4+10)/(3√(2)-4)\\\\\\=((4-5)√(2)+6)/(3√(2)-4)\\\\\\=(-1√(2)+6)/(3√(2)-4)$

Wjmolina answered Sep 28, 2021

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