Bài 24 trang 15 - Rút gọn và tìm giá trị

Lời giải:

a) √4(1+6x+9x2)2=√4.[(3x+1)2]2=√22(3x+1)441+6�+9�22=4.3�+122=223�+14

= √22.√(3x+1)422.3�+14 = 2(3x + 1)²

Thay x = −√2-2, ta có:

2.(−3√2-32 + 1)² = 2.[(−3√2)2−2.3√2+1]−322−2.32+1

= 2.(18 - 6√22 + 1) = 38 - 12√22 ≈ 21,032

b) √9a2(b2+4−4b)=√9a2.(b−2)2=√9.√a2.√(b−2)29�2�2+4−4�=9�2.�−22=9.�2.�−22 = 3.|a|.|b - 2|

Thay a = -2; b = −√3-3, ta có:

3.|-2|.∣∣−√3−2∣∣−3−2 = 3.2.(√33 + 2) = 6√33 + 12 ≈ 22,392