Toán Lớp 9: Rút gọn :
√ 6 + 2 √5 – √6 – 2√5
√11+ 6 √2 – √ 11 – 6√2
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Toán Lớp 9: Rút gọn :
√ 6 + 2 √5 – √6 – 2√5
√11+ 6 √2 – √ 11 – 6√2
Comments ( 2 )
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a)
sqrt6+2sqrt5-sqrt6-2sqrt5
=sqrt6 -sqrt6 +2sqrt5 -sqrt5
=0
b) sqrt11+6sqrt2 -sqrt11-6sqrt2
=sqrt11-sqrt11+6sqrt2-6sqrt2
=0
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a)
sqrt{6+2sqrt5}-{sqrt6-2sqrt5}
=sqrt{5+2sqrt5+1}-sqrt{5-2sqrt5+1}
=sqrt{(sqrt5)^2+2*sqrt5*1+1^2}-sqrt{(sqrt5)^2-2*sqrt5*1+1^2}
=sqrt{(sqrt5+1)^2}-sqrt{(sqrt5-1)^2}
=|sqrt5+1|-|sqrt5-1|
=sqrt5+1-sqrt5+1 (Vì sqrt5+1>0 ; sqrt5-1>0 )
=2
b)
sqrt{11+6sqrt2}-sqrt{11-6sqrt2}
=sqrt{9+6sqrt2+2}-sqrt{9-6sqrt2+2}
=sqrt{3^2+2*3*sqrt2+(sqrt2)^2}-sqrt{3^2-2*3*sqrt2+(sqrt2)^2}
=sqrt{(3+sqrt2)^2}-sqrt{(3-sqrt2)^2}
=|3+sqrt2|-|3-sqrt2|
=3+sqrt2-3+sqrt2 (Vì 3+sqrt2>0 ; 3-sqrt2>0 )
=2sqrt2