а)
(√15 + √10) * 2√5 - 5√12 =
= (√3*5 + √2*5) * 2√5 - 5√12 =
= √3*5 * 2√5 + √2*5 * 2√5 - 5√(3*4) =
= 2*5√3 + 2*5√2 - 2*5√3 =
= 10√3 + 10√2 - 10√3 = 10√2,
б)
(2√70 - 2√28) / (3√35 - 3√14) =
= (2√(35*2) - 2√(14*2)) / (3√35 - 3√14) =
= (2√2 * (√35 - √14)) / (3 * (√35 - √14)) = (2√2) / 3
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Answers & Comments
а)
(√15 + √10) * 2√5 - 5√12 =
= (√3*5 + √2*5) * 2√5 - 5√12 =
= √3*5 * 2√5 + √2*5 * 2√5 - 5√(3*4) =
= 2*5√3 + 2*5√2 - 2*5√3 =
= 10√3 + 10√2 - 10√3 = 10√2,
б)
(2√70 - 2√28) / (3√35 - 3√14) =
= (2√(35*2) - 2√(14*2)) / (3√35 - 3√14) =
= (2√2 * (√35 - √14)) / (3 * (√35 - √14)) = (2√2) / 3