Problema Solution
Show by substitution that 1+√ 2 and 1-√ 2 are roots of 2xsquared-4x+1=0
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2 2
Answer provided by our tutors
2(1+√ 2/2)^2 - 4(1+√ 2/2) + 1 =
= 2(1 + 2√ 2/2 + 2/4) - 4 - 2√ 2 + 1 =
= 2 + 2√ 2 + 1 - 4 - 4√ 2 + 1 = 0
2(1 - √ 2/2)^2 - 4(1-√ 2/2) + 1 =
= 2(1 - 2√ 2/2 + 2/4) - 4 + 2√ 2 + 1 =
= 2 - 2√ 2 + 1 - 4 + 2√ 2 + 1 = 0