/2x-5/=3.x+2
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Bài 1.
a. $=a^2+2.a.12+12^2=a^2+24a+144$
b. $=(3a)^2+2.3a.\frac{1}{3}+(\frac{1}{3})^2=9a^2+2a+\frac{1}{9}$
c. $=(5a^2)^2+2.5a^2.6+6^2=25a^4+60a^2+36$
d. $=\frac{1}{4}+2.\frac{1}{2}.4b+(4b)^2$
$=\frac{1}{4}+4b+16b^2$
e.
$=(a^m)^2+2.a^m.b^n+(b^n)^2$
$=a^{2m}+2a^mb^n+b^{2n}$
Bài 2.
$(x-0,3)^2=x^2-0,6x+0,09$
$(6x-3y)^2=36x^2-36xy+9y^2$
$(5-2xy)^2=25-20xy+4x^2y^2$
$(x^4-1)^2=x^8-2x^4+1$
$(x^5-y^3)^2=x^{10}-2x^5y^3+y^6$
\(\dfrac{x}{6}=\dfrac{7}{4}\Rightarrow x=\dfrac{6\cdot7}{4}=\dfrac{21}{2}\\ \dfrac{3}{x}=\dfrac{21}{17}\Rightarrow x=\dfrac{3\cdot17}{21}=\dfrac{17}{7}\)
5:
a: sin x=2*cosx
\(A=\dfrac{6cosx+2cosx-4\cdot8\cdot cos^3x}{cos^3x-2cosx}\)
\(=\dfrac{8-32cos^2x}{cos^2x-2}\)
b: VT=sin^4(pi/2-x)+cos^4(x+pi/2)+6*1/2*sin^22x+1/2*cos4x
=cos^4x+sin^4x+3*sin^2(2x)+1/2*(1-2*sin^2(2x))
=1-2*sin^2x*cos^2x+3*sin^2(2x)+1/2-sin^2(2x)
==3/2=VP
\(\Leftrightarrow\left\{{}\begin{matrix}x-2y+z=2\\4y-4z=-6\\-y+z=-13\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2y+z=2\\y-z=-\dfrac{3}{2}\\-y+z=-13\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2y+z=2\\y-z=-\dfrac{3}{2}\\0=-\dfrac{29}{2}\end{matrix}\right.\)
Hệ đã cho vô nghiệm
Câu 5:
Áp dụng định lí cos: \(bc\cdot\cos A=bc\cdot\dfrac{b^2+c^2-a^2}{2bc}=\dfrac{b^2+c^2-a^2}{2}\)
Tương tự \(\Leftrightarrow ac\cdot\cos B=\dfrac{c^2+a^2-b^2}{2};ab\cdot\cos C=\dfrac{a^2+b^2-c^2}{2}\)
\(\Leftrightarrow P=\dfrac{a^2+b^2-c^2+b^2+c^2-a^2+c^2+a^2-b^2}{2}=\dfrac{a^2+b^2+c^2}{2}=\dfrac{4032}{2}=2016\)
Bài 13:
$6-2\sqrt{5}=5-2\sqrt{5}.\sqrt{1}+1$
$=(\sqrt{5}-1)^2$
Tương tự: $6+2\sqrt{5}=(\sqrt{5}+1)^2$
Do đó:
$M=\sqrt{(\sqrt{5}+1)^2}-\sqrt{(\sqrt{5}-1)^2}$
$=|\sqrt{5}+1|-|\sqrt{5}-1|=(\sqrt{5}+1)-(\sqrt{5}-1)$
$=2$
Bài 14:
a.
$M=\sqrt{4+2\sqrt{4}.\sqrt{5}+5}-\sqrt{4-2\sqrt{4}.\sqrt{5}+5}$
$=\sqrt{(\sqrt{4}+\sqrt{5})^2}-\sqrt{(\sqrt{4}-\sqrt{5})^2}$
$=|\sqrt{4}+\sqrt{5}|-|\sqrt{4}-\sqrt{5}|$
$=2+\sqrt{5}-(\sqrt{5}-2)=4$
b.
$N=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}$
$=\sqrt{(\sqrt{7}-1)^2}-\sqrt{(\sqrt{7}+1)^2}$
$=|\sqrt{7}-1|-|\sqrt{7}+1|$
$=(\sqrt{7}-1)-(\sqrt{7}+1)=-2$
+ Nếu \(2x-5\ge0\Leftrightarrow x\ge\frac{5}{2}\)
\(\Rightarrow2x-5=3x+2\Leftrightarrow x=-7< \frac{5}{2}\) (Loại)
+ Nếu \(2x-5< 0\Leftrightarrow x< \frac{5}{2}\)
\(\Rightarrow-2x+5=3x+2\Leftrightarrow x=\frac{3}{5}< \frac{5}{2}\)
Trả lời :
|2x - 5| = 3x + 2
Do |2x - 5| > 0
=> 3x + 2 > 0
=> 2x - 5 = 3x + 2
=> 5 - 2 = 3x - 2x
=> x = 3
Vậy x = 3.
~Std well~
#Tiểu Hàm