( x - 1/2)^3=-8/27
Những câu hỏi liên quan
a/ (x-1/2)mũ 3 = -8 e/(x-5/2) mũ 3=-1/8
b/ (x-1/3)mũ 3=27/8 f/(x-1/8) mũ 3=-8/125
c/ (x-5/2)mũ 3=-8/27 giúp mk vs!!!!!!!!!! plsssss
d/ (x-1/3) mũ 3=8/27
Ok bro, mấy câu này là giải phương trình dạng lập phương kiểu:
\(\left(\right. x - a \left.\right)^{3} = b \Rightarrow x = a + \sqrt[3]{b}\)
Tớ sẽ giải lần lượt từng câu cho gọn gàng nha:
a/\(\left(\right. x - \frac{1}{2} \left.\right)^{3} = - 8\)\(x - \frac{1}{2} = \sqrt[3]{- 8} = - 2 \Rightarrow x = - 2 + \frac{1}{2} = \boxed{- \frac{3}{2}}\)
\(\left(\right. x - \frac{5}{2} \left.\right)^{3} = - \frac{1}{8}\)\(x - \frac{5}{2} = \sqrt[3]{- \frac{1}{8}} = - \frac{1}{2} \Rightarrow x = \frac{5}{2} - \frac{1}{2} = \boxed{2}\)
b/\(\left(\right. x - \frac{1}{3} \left.\right)^{3} = \frac{27}{8}\)\(x - \frac{1}{3} = \sqrt[3]{\frac{27}{8}} = \frac{3}{2} \Rightarrow x = \frac{1}{3} + \frac{3}{2} = \frac{11}{6} \Rightarrow \boxed{x = \frac{11}{6}}\)
\(\left(\right. x - \frac{1}{8} \left.\right)^{3} = - \frac{8}{125}\)\(x - \frac{1}{8} = \sqrt[3]{- \frac{8}{125}} = - \frac{2}{5} \Rightarrow x = \frac{1}{8} - \frac{2}{5} = \boxed{- \frac{11}{40}}\)
c/\(\left(\right. x - \frac{5}{2} \left.\right)^{3} = - \frac{8}{27}\)
\(x - \frac{5}{2} = \sqrt[3]{- \frac{8}{27}} = - \frac{2}{3} \Rightarrow x = \frac{5}{2} - \frac{2}{3} = \frac{15 - 4}{6} = \boxed{\frac{11}{6}}\)
d/\(\left(\right. x - \frac{1}{3} \left.\right)^{3} = \frac{8}{27}\)
\(x - \frac{1}{3} = \sqrt[3]{\frac{8}{27}} = \frac{2}{3} \Rightarrow x = \frac{1}{3} + \frac{2}{3} = \boxed{1}\)
✅ Tóm tắt đáp án:
Câu | Đáp án |
|---|---|
a1 | \(x = - \frac{3}{2}\)x=−32x = -\frac{3}{2} |
a2 | \(x = 2\)x=2x = 2 |
b1 | \(x = \frac{11}{6}\)x=116x = \frac{11}{6} |
b2 | \(x = - \frac{11}{40}\)x=−1140x = -\frac{11}{40} |
c | \(x = \frac{11}{6}\)x=116x = \frac{11}{6} |
d | \(x = 1\)x=1x = 1 |
Có cần mình hướng dẫn cách bấm máy tính để ra nhanh hơn không bro?
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Ok bro, mấy câu này là giải phương trình dạng lập phương kiểu:
\(\left(\right. x - a \left.\right)^{3} = b \Rightarrow x = a + \sqrt[3]{b}\)
Tớ sẽ giải lần lượt từng câu cho gọn gàng nha:
a/\(\left(\right. x - \frac{1}{2} \left.\right)^{3} = - 8\)\(x - \frac{1}{2} = \sqrt[3]{- 8} = - 2 \Rightarrow x = - 2 + \frac{1}{2} = \boxed{- \frac{3}{2}}\)
\(\left(\right. x - \frac{5}{2} \left.\right)^{3} = - \frac{1}{8}\)\(x - \frac{5}{2} = \sqrt[3]{- \frac{1}{8}} = - \frac{1}{2} \Rightarrow x = \frac{5}{2} - \frac{1}{2} = \boxed{2}\)
b/\(\left(\right. x - \frac{1}{3} \left.\right)^{3} = \frac{27}{8}\)\(x - \frac{1}{3} = \sqrt[3]{\frac{27}{8}} = \frac{3}{2} \Rightarrow x = \frac{1}{3} + \frac{3}{2} = \frac{11}{6} \Rightarrow \boxed{x = \frac{11}{6}}\)
\(\left(\right. x - \frac{1}{8} \left.\right)^{3} = - \frac{8}{125}\)\(x - \frac{1}{8} = \sqrt[3]{- \frac{8}{125}} = - \frac{2}{5} \Rightarrow x = \frac{1}{8} - \frac{2}{5} = \boxed{- \frac{11}{40}}\)
c/\(\left(\right. x - \frac{5}{2} \left.\right)^{3} = - \frac{8}{27}\)
\(x - \frac{5}{2} = \sqrt[3]{- \frac{8}{27}} = - \frac{2}{3} \Rightarrow x = \frac{5}{2} - \frac{2}{3} = \frac{15 - 4}{6} = \boxed{\frac{11}{6}}\)
d/\(\left(\right. x - \frac{1}{3} \left.\right)^{3} = \frac{8}{27}\)
\(x - \frac{1}{3} = \sqrt[3]{\frac{8}{27}} = \frac{2}{3} \Rightarrow x = \frac{1}{3} + \frac{2}{3} = \boxed{1}\)
✅ Tóm tắt đáp án:
Câu | Đáp án |
|---|---|
a1 | \(x = - \frac{3}{2}\)x=−32x = -\frac{3}{2} |
a2 | \(x = 2\)x=2x = 2 |
b1 | \(x = \frac{11}{6}\)x=116x = \frac{11}{6} |
b2 | \(x = - \frac{11}{40}\)x=−1140x = -\frac{11}{40} |
c | \(x = \frac{11}{6}\)x=116x = \frac{11}{6} |
d | \(x = 1\)x=1x = 1 |
Có cần mình hướng dẫn cách bấm máy tính để ra nhanh hơn không bro?
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\(\dfrac{1}{27}+a^3\\ 8x^3+27y^3\\ \dfrac{1}{8}x^3+8y^3\\ x^6+1\\ x^9+1\\ x^3-64\\ x^3-125\\ 8x^6-27y^3\\ \dfrac{1}{64}x^6-125y^3\\ \dfrac{1}{8}x^3-8\\ x^3+6x^2+12x+8\\ x^3+9x^2+27x+27\) Giúp mình với mình cần gấp ;-;
1) \(\dfrac{1}{27}+a^3=\left(\dfrac{1}{3}+a\right)\left(\dfrac{1}{9}-\dfrac{a}{3}+a^2\right)\)
2) \(=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
3) \(=\left(\dfrac{1}{2}x+2y\right)\left(\dfrac{1}{4}x-xy+4y^2\right)\)
4) \(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
5) \(=\left(x^3+1\right)\left(x^6-x^3+1\right)\)
6) \(=\left(x-4\right)\left(x^2+4x+16\right)\)
7) \(=\left(x-5\right)\left(x^2+5x+25\right)\)
8) \(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
9) \(=\left(\dfrac{1}{4}x^2-5y\right)\left(\dfrac{1}{16}x^4+\dfrac{5}{4}x^2y+25y^2\right)\)
10) \(=\left(\dfrac{1}{2}x-2\right)\left(\dfrac{1}{4}x^2+x+4\right)\)
11) \(=\left(x+2\right)^3\)
12) \(=\left(x+3\right)^3\)
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Tính:
a) 2^5 x 13^12 x 7^8 : 27 x 13^10 x 7^9
b) 2^n x 11 x 3 : 6^n x 3
c) 5^5 x 7 x 9^5 : 15^10
d) 7 x 8^10 x 27^9 - 8 x 9^13 x 2^27 : 7 x 6^26 x 2^2 - 2^4 x 8^3 x 27^9
e) 2^2^1^2015
f) 2015^0^2015^0^2015
72-8/3 bằng bao nhiêu số tự nhiên
a) 3 x X x 2/3 = 4/5
b) 3,94 x 18,24 + 18,24 x 3,72 + 18,24 x 2,34
c) 8/9 + 14/27 + 1/9 + 13/27
d) 8/19 x 2/7 + 8/19 x 1/7 + 8/19 x 4/7
a) 3 x X x 2/3 = 4/5
3.x=6/5
x=2/5
b) 3,94 x 18,24 + 18,24 x 3,72 + 18,24 x 2,34
=18,24(3,94+3,72+2,34)
=18,24.10
=182,4
d) 8/19 x 2/7 + 8/19 x 1/7 + 8/19 x 4/7
=8/19(2/7+1/7+4/7)
=8/19.1
=8/19
a)\(3xXx\frac{2}{3}=\frac{4}{5}\) b)\(3,94x18,24+18,24x3,72+18,24x2,34\)
\(3xX=\frac{4}{5}:\frac{2}{3}\) \(=18,24x\left(3,94+3,72+2,34\right)\)
\(3xX=\frac{6}{5}\) \(=18,24x10\)
\(X=\frac{6}{5}:3\) \(=182,4\)
\(X=\frac{2}{5}\)
Toàn nói bậy vậy lam 2212 .
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(1/16)^-2 x 1/8 + 49^(-2) x (1/7)^(-3) + 36^(-2) x 8^(-2) x 27
Lời giải:
Gọi biểu thức là A.
\(A=256.\frac{1}{8}+\frac{1}{49^2}.7^3+\frac{1}{36^2}.\frac{1}{8^2}.27\\ =32+\frac{1}{7}+\frac{1}{3072}=32\frac{3079}{21504}\)
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Tìm X
A, (X+1)(X+2)(X+5) - X^2(X+8)=27
B, 1/4 X^2-(1/2X-4)1/2X=-14
C, 3(1-4X)(X-1)+4(3X-2)(X+3)=-27
D,(X+3)(X^2-3X+9) - X(X-1)(X+1)=27
Tính nhanh: LƯU Ý tất cả số dưới đây đều là phân số
1,1/8 x 2/5 + 3/5 + 1/8
2,( -1)/15 x 2/5 + (-5)/3 x (-1)/13
3,4/9 : 11/6 + 5/9 x 6/11
4,5/19 x 7/13 + 7/19 x 8/13 - 3 x 7/19
5, 2/7 x 4/23 - 2/7 x 27/23 + 2/7
6,3/8 x 3/7 +3/8 x 4/7 + 11/8
7,-5/27 : 6/11 - 16/11 x 5/27 - 5/27
8, 5/16 x 7/8 - 5/16 x 1/8 + 10/8 :16/5
9,1/3 x 39/17 - 129/3 x 1/17
10,5/2 : 23/3 - 3/2 x 7/23
2: \(=\dfrac{-2}{75}+\dfrac{5}{39}=\dfrac{33}{325}\)
3: \(=\dfrac{6}{11}\left(\dfrac{4}{9}+\dfrac{5}{9}\right)=\dfrac{6}{11}\)
4: \(=\dfrac{7}{19}\left(\dfrac{5}{13}+\dfrac{8}{13}-1\right)=-2\cdot\dfrac{7}{19}=-\dfrac{14}{19}\)
5: \(=\dfrac{2}{7}\left(\dfrac{4}{23}-\dfrac{27}{23}+1\right)=0\)
6: \(=\dfrac{3}{8}\left(\dfrac{3}{7}+\dfrac{4}{7}\right)+\dfrac{11}{8}=\dfrac{3}{8}+\dfrac{11}{8}=\dfrac{14}{8}=\dfrac{7}{4}\)
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\(\left(3-x\right)^3=-\dfrac{27}{64};\left(x-5\right)^3=\dfrac{1}{-27};\left(x-\dfrac{1}{2}\right)^3=\dfrac{27}{8};\left(2x-1\right)^2=\dfrac{1}{4};\left(2-3x\right)^2=\dfrac{9}{4};\left(1-\dfrac{2}{3}\right)^2=\dfrac{4}{9}\)
\(\left(3-x\right)^3=-\dfrac{27}{64}\)
\(\left(3-x\right)^3=\left(\dfrac{-3}{4}\right)^3\)
\(=>3-x=\dfrac{-3}{4}\)
\(x=3-\dfrac{-3}{4}=\dfrac{12}{4}+\dfrac{3}{4}\)
\(x=\dfrac{15}{4}\)
________
\(\left(x-5\right)^3=\dfrac{1}{-27}\)
\(\left(x-5\right)^3=\left(\dfrac{-1}{3}\right)^3\)
\(=>x-5=\dfrac{-1}{3}\)
\(x=\dfrac{-1}{3}+5=\dfrac{-1}{3}+\dfrac{15}{3}\)
\(x=\dfrac{14}{3}\)
_____________
\(\left(x-\dfrac{1}{2}\right)^3=\dfrac{27}{8}\)
\(\left(x-\dfrac{1}{2}\right)^3=\left(\dfrac{3}{2}\right)^3\)
\(=>x-\dfrac{1}{2}=\dfrac{3}{2}\)
\(x=\dfrac{3}{2}+\dfrac{1}{2}\)
\(x=2\)
________
\(\left(2x-1\right)^2=\dfrac{1}{4}\)
\(\left(2x-1\right)^2=\left(\dfrac{1}{2}\right)^2\) hoặc \(\left(2x-1\right)^2=\left(\dfrac{-1}{2}\right)^2\)
\(=>2x-1=\dfrac{1}{2}\) \(2x-1=\dfrac{-1}{2}\)
\(2x=\dfrac{1}{2}+1=\dfrac{1}{2}+\dfrac{2}{2}\) \(2x=\dfrac{-1}{2}+1=\dfrac{-1}{2}+\dfrac{2}{2}\)
\(2x=\dfrac{3}{2}\) \(2x=\dfrac{1}{2}\)
\(x=\dfrac{3}{2}:2=\dfrac{3}{2}.\dfrac{1}{2}\) \(x=\dfrac{1}{2}:2=\dfrac{1}{2}.\dfrac{1}{2}\)
\(x=\dfrac{3}{4}\) \(x=\dfrac{1}{4}\)
____________
\(\left(2-3x\right)^2=\dfrac{9}{4}\)
\(\left(2-3x\right)^2=\left(\dfrac{3}{2}\right)^2\) hoặc \(\left(2-3x\right)^2=\left(\dfrac{-3}{2}\right)^2\)
\(=>2-3x=\dfrac{3}{2}\) \(2-3x=\dfrac{-3}{2}\)
\(3x=2-\dfrac{3}{2}=\dfrac{4}{2}-\dfrac{3}{2}\) \(3x=2-\dfrac{-3}{2}=\dfrac{4}{2}+\dfrac{3}{2}\)
\(3x=\dfrac{1}{2}\) \(3x=\dfrac{7}{2}\)
\(x=\dfrac{1}{2}.\dfrac{1}{3}\) \(x=\dfrac{7}{2}.\dfrac{1}{3}\)
\(x=\dfrac{1}{6}\) \(x=\dfrac{7}{6}\)
______________
\(\left(1-\dfrac{2}{3}\right)^2=\dfrac{4}{9}\) -> Kiểm tra đề câu này
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(3-x)3=(-\(\dfrac{3}{4}\))3
3-x=-\(\dfrac{3}{4}\)
x=3-(-\(\dfrac{3}{4}\))
x=\(\dfrac{15}{4}\)
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Tìm x
1/ (x - 1/2)^3 = 8
2/ (x - 1)^3 = 8/27
3/ (x - 2/3)^x = 1/81
1)
Ta có: \(\left(x-\frac{1}{2}\right)^3=8\Rightarrow\left(x-\frac{1}{2}\right)^3=2^3\)
\(\Rightarrow x-\frac{1}{2}=2\Rightarrow x=2+\frac{1}{2}=\frac{5}{2}\)
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\(\left(x-1\right)^3=\frac{8}{27}\Rightarrow\left(x-1\right)^3=\left(\frac{2}{3}\right)^3\)
\(\Rightarrow x-1=\frac{2}{3}\Rightarrow x=\frac{2}{3}+1=\frac{5}{3}\)
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SGK Cánh Diều trang 67
17 tháng 9 2023 lúc 15:38
Tính:
a) \((6{x^2} - 2x + 1):(3x - 1)\);
b) \((27{x^3} + {x^2} - x + 1):( - 2x + 1)\);
c) \((8{x^3} + 2{x^2} + x):(2{x^3} + x + 1)\);
d) \((3{x^4} + 8{x^3} - 2{x^2} + x + 1):(3x + 1)\)
