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

1 Answer

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)

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