Đáp án:
Giải thích các bước giải:
Bài 1:
a)√125 - 2√20 - 3√80 + 4√45
=5√5 - 4√5 -12√5 + 12√5
=√5.(5-4-12+12)=√5
b)√(√2+1)² +√(5-2√6)
=√2+1+√(√3-√2)²
=√2+1+√3-√2 (√3>√2)
=1+√3
c)(√15 - √12)/(√5 - 2)-(6+2√6)/(√3 + √2)
=√3(√5 -√4)/(√5 - 2)-(6+2√6)(√3-√2)/(√3 + √2)(√3-√2)
=√3(√5 -2)/(√5 - 2)-(6√3-6√2+2√18-2√12)/(3-2)
=√3-6√3+6√2-2√18+2√12
=-5√3+6√2-6√2+4√3=-√3
Bài 2:
√(27x-9)-√(3x-1)=8-√(12x-4) (ĐK:x≥1/3)
⇔3√(3x-1)-√(3x-1)+2√(3x-1)=8
⇔4√(3x-1)=8
⇔√(3x-1)=2
⇔3x-1=4⇒x=5/3(tmđk)
Vậy...
Bài 3:
A=9+4√5/√5+2 - 9-4√5/√5 - 2 -√(3-√5)/√2
=(9+4√5)(√5 - 2)-(9-4√5)(√5+2)/(√5 - 2)(√5 +2) -√((3-√5).2)/2
=9√5-18+20-8√5-9√5-18+20+8√5 - √(6-2√5)/2
=4-√(√5-1)²/2
=4-(√5 -1)/2=(8-√5 +1)/2=(9-√5)/2
