Question

6. Calculaţi:

D) (9/(2sqrt(6)) - 8/(3sqrt(6)) - 4/(sqrt(6))) - (16/(5sqrt(6)) - 33/(10sqrt(6))) - (3/(sqrt(6)) - 8/(3sqrt(6))) b)

(18/(3sqrt(3)) - 6/(2sqrt(3)) + 2/(sqrt(3))) - (12/(sqrt(3)) + 5/(2sqrt(3)) - 4/(3sqrt(3)))

(13/(5sqrt(2)) + 6/(3sqrt(2))) - (26/(3sqrt(2)) + 6/(4sqrt(2)) - 7/(sqrt(2)))

4) (8/(5sqrt(6)) - 4/(sqrt(24)) - 16/(15sqrt(6))) - (8/(3sqrt(54)) - 6/(sqrt(54))) Mano

d)

c)

a)​

Answer 1

Rationalizam-  amplificam cu numitorul

a)

$\frac{8\sqrt{6} }{30} -\frac{4\sqrt{24} }{24} -\frac{16\sqrt{6} }{90} -(\frac{8\sqrt{54} }{162} -\frac{6\sqrt{54} }{54} )=\\\\\frac{4\sqrt{6} }{15} -\frac{\sqrt{24} }{6} -\frac{8\sqrt{6} }{45} -(\frac{4\sqrt{54} }{81} -\frac{\sqrt{54} }{9} )=$

Aducem la acelasi numitor comun

$\frac{24\sqrt{6}-15\sqrt{24} -16\sqrt{6} }{90} -\frac{4\sqrt{54} -9\sqrt{54} }{81} =\\\\\frac{-22\sqrt{6} }{90} +\frac{5\sqrt{54} }{81} =\\\\\frac{-11\sqrt{6} }{45} +\frac{15\sqrt{6} }{81} =\frac{-99\sqrt{6}+75\sqrt{6} }{405} =-\frac{24\sqrt{6} }{405} =-\frac{8\sqrt{6} }{135}$

b)

$\frac{9\sqrt{6} }{12} -\frac{8\sqrt{6} }{18} -\frac{4\sqrt{6} }{6} -(\frac{16\sqrt{6} }{30} -\frac{33\sqrt{6} }{60} )-(\frac{3\sqrt{6} }{6} -\frac{8\sqrt{6} }{18})=$

Aducem la acelasi numitor comun:

$\frac{135\sqrt{6}-80\sqrt{6} -120\sqrt{6}-96\sqrt{6}+99\sqrt{6} -90\sqrt{6} +80\sqrt{6} }{180} =-\frac{72\sqrt{6} }{180} =-\frac{2\sqrt{6} }{5}$

c)

$\frac{18\sqrt{3} }{9} -\frac{6\sqrt{3} }{6} +\frac{2\sqrt{3} }{3} -(\frac{12\sqrt{3} }{3} +\frac{5\sqrt{3} }{6} -\frac{4\sqrt{3} }{9} )=$

Aducem la acelasi numitor comun:

$\frac{36\sqrt{3} -18\sqrt{3}+12\sqrt{3} -72\sqrt{3} -15\sqrt{3} +8\sqrt{3} }{18} =-\frac{49\sqrt{3} }{18}$

Acelasi lucru faci si la punctul d

Un alt exercitiu gasesti aici: https://brainly.ro/tema/1757330

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