Question by Fake Love - Discuss with MathYouLike

Fake Love

26/12/2017 at 15:47

Shorten the following expressions:

a) $2 \sqrt{a^{2}} - 5 a$ with a < 0. b) $\sqrt{25 a^{2}}$ + 3a with a ≥ 0.

c) $\sqrt{9 a^{4}} + 3 a^{2}$ d) $5 \sqrt{4 a^{6}}$ - $3 a^{3}$ with a < 0

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Trần Thủy Tiên 26/12/2017 at 15:50

a)

2√a2−5a=2|a|−5a2a2−5a=2|a|−5a

2|a|−5a=−2a−5a=−7a2|a|−5a=−2a−5a=−7a

b)

√9a4+3a2=3|a2|+3a2=6a29a4+3a2=3|a2|+3a2=6a2

because a2≥0∀aϵR⇔|a2|=a2a2≥0∀aϵR⇔|a2|=a2

c)

√25a2+3a=5|a|+3a=5a+3a=8a25a2+3a=5|a|+3a=5a+3a=8a

because a≥0⇒|a|=aa≥0⇒|a|=a

d)

5√4a6−3a354a6−3a3

=5.2.|a3|−3a3=5.2.|a3|−3a3

=10.(−a)3−3a3=−13a3=10.(−a)3−3a3=−13a3

because a<0a<0 so |a3|=−a3
KEITA FC 8C 27/12/2017 at 19:14
- a)
  
  2√a2−5a=2|a|−5a2a2−5a=2|a|−5a
  
  2|a|−5a=−2a−5a=−7a2|a|−5a=−2a−5a=−7a
  
  b)
  
  √9a4+3a2=3|a2|+3a2=6a29a4+3a2=3|a2|+3a2=6a2
  
  because a2≥0∀aϵR⇔|a2|=a2a2≥0∀aϵR⇔|a2|=a2
  
  c)
  
  √25a2+3a=5|a|+3a=5a+3a=8a25a2+3a=5|a|+3a=5a+3a=8a
  
  because a≥0⇒|a|=aa≥0⇒|a|=a
  
  d)
  
  5√4a6−3a354a6−3a3
  
  =5.2.|a3|−3a3=5.2.|a3|−3a3
  
  =10.(−a)3−3a3=−13a3=10.(−a)3−3a3=−13a3
  
  because a<0a<0 so |a3|=−a3
  2

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