设三角形ABC的内角A、B、C的对边长分别为abc,且3b^2+3c^2-3a^2=4(根号下2)bca)求SinA的值 b)求[2sin(A+π/4)sin(B+C+π/4)]/1-cos2A的值._百度作业帮
设三角形ABC的内角A、B、C的对边长分别为abc,且3b^2+3c^2-3a^2=4(根号下2)bca)求SinA的值 b)求[2sin(A+π/4)sin(B+C+π/4)]/1-cos2A的值.
设三角形ABC的内角A、B、C的对边长分别为abc,且3b^2+3c^2-3a^2=4(根号下2)bca)求SinA的值&b)求[2sin(A+π/4)sin(B+C+π/4)]/1-cos2A的值.
余弦定理CosA = (b^2+c^2-a^2)/(2bc) = 2/3 * 根号(2)所以(SinA)^2 = 1-(CosA)^2 = 1 - 8/9 = 1/9所以SinA = 1/3
因为A是 0~π的角,SinA>0 2B+C = π - A所以分子变为2Sin(A + π/4)Sin(π - A + π/4) = 2Sin(A + π/4) Sin(A-π/4) = - (Cos(A + π/4 + A - π/4) - Cos(A + π/4 - A + π/4) = - (Cos2A -0) = -Cos2A则原式化为Cos2A/(Cos2A-1) 而Cos2A = 1-2(SinA)^2
二倍角公式SinA = 1/3所以Cos2A = 1 - 2/9 = 7/9那么原式 = 7/9
/ (7/9 -1) = -7/2正数a,b,c 且a+b+c=1,求证:√(3a^2+1)+√(3b^2+1)+√(3c^2+1)>2√3_百度作业帮
正数a,b,c 且a+b+c=1,求证:√(3a^2+1)+√(3b^2+1)+√(3c^2+1)>2√3
正数a,b,c 且a+b+c=1,求证:√(3a^2+1)+√(3b^2+1)+√(3c^2+1)>2√3
用均值不等式，3a^2+1≥2√3a^2=2a√3即√（3a^2+1）+√(3b^2+1)+√(3c^2+1)≥2a√3+2b√3+2c√3=2（a+b+c)√3=2√3所以：√（3a^2+1）+√(3b^2+1)+√(3c^2+1)≥2√3最好用柯西不等式和均值不等式解.1.已知n是正整数,求证：n（n+1开n次方-1）＜1+1/2+…+1/n＜n-n-1/n开n-1次方2.a,b,c,d满足a-2b+3c-d=5 2a²+3b²+2c²+6d²=10 求证 十三分之5减4倍根号30小于等于_百度作业帮
最好用柯西不等式和均值不等式解.1.已知n是正整数,求证：n（n+1开n次方-1）＜1+1/2+…+1/n＜n-n-1/n开n-1次方2.a,b,c,d满足a-2b+3c-d=5 2a²+3b²+2c²+6d²=10 求证 十三分之5减4倍根号30小于等于
最好用柯西不等式和均值不等式解.1.已知n是正整数,求证：n（n+1开n次方-1）＜1+1/2+…+1/n＜n-n-1/n开n-1次方2.a,b,c,d满足a-2b+3c-d=5 2a²+3b²+2c²+6d²=10 求证 十三分之5减4倍根号30小于等于a小于等于十三分之5加四倍根号三十
1,要证n（n+1）开n次方-1)已知a,b,c均为正数,证明：a^2+b^2+c^2+（1/a+1/b+1/c）^2>=6√3_百度作业帮
已知a,b,c均为正数,证明：a^2+b^2+c^2+（1/a+1/b+1/c）^2>=6√3
已知a,b,c均为正数,证明：a^2+b^2+c^2+（1/a+1/b+1/c）^2>=6√3
证明：a^2+b^2+c^2+(1/a+1/b+1/c)^2=a^2+b^2+c^2+1/a^2+1/b^2+1/c^2+2/ab+2/bc+2/ca 由均值不等式：1/a^2+1/b^2>=2/ab1/b^2+1/c^2>=2/bc1/c^2+1/a^2>=2/ca 上三式相加得2(1/a^2+1/b^2+1/c^2)>=2(1/ab+1/bc+1/ca)也即1/a^2+1/b^2+1/c^2>=1/ab+1/bc+1/ca所以a^2+b^2+c^2+1/a^2+1/b^2+1/c^2+2/ab+2/bc+2/ca>=a^2+b^2+c^2+3(1/ab+1/bc+1/ca)=(a^2+3/ab)+(b^2+3/bc)+(c^2+3/ca)>=2√(3a/b)+2√(3b/c)+2√(3c/a)>=6√3得证.
证明： （证法一） 因为a，b，c均为正数，由平均值不等式得 {a2+b2+c2≥3(abc)231a+1b+1c≥3(abc)-13① 所以 (1a+1b+1c)2≥9(abc)-23②（ 故 a2+b2+c2+(1a+1b+1c)2≥3(abc)23+9(abc)-23． 又 3(abc)23+9(abc)-23≥227=63③ 所以...初中乘法公式的一些题目1.（5-3m)²2.(-5ayz+1/5a²)²3.(a+b)²(a-b)²(a²+b²)²4.（a-b-c)²5.(2a+3b-4c)²6.(a+b+c+d)(a+b-c-d)7.(a+b+c+d)²8.(x+y)(x-y)9.(3x+2y)(3x-2y)10.(-3x+2y)(-3x-2y)11.(7mn&s_百度作业帮
初中乘法公式的一些题目1.（5-3m)²2.(-5ayz+1/5a²)²3.(a+b)²(a-b)²(a²+b²)²4.（a-b-c)²5.(2a+3b-4c)²6.(a+b+c+d)(a+b-c-d)7.(a+b+c+d)²8.(x+y)(x-y)9.(3x+2y)(3x-2y)10.(-3x+2y)(-3x-2y)11.(7mn&s
初中乘法公式的一些题目1.（5-3m)²2.(-5ayz+1/5a²)²3.(a+b)²(a-b)²(a²+b²)²4.（a-b-c)²5.(2a+3b-4c)²6.(a+b+c+d)(a+b-c-d)7.(a+b+c+d)²8.(x+y)(x-y)9.(3x+2y)(3x-2y)10.(-3x+2y)(-3x-2y)11.(7mn²-8cd²)(7m²n+8cd²)12.1/5(30a²+15b²)(6a²-3b²)13.(x+2y-3)(x-2y+3)14.(x+1/x)²-(x-1/x)²15.(2a-b)²-2b²16.(5m+3n)²-(2m-n)²17.[(a+b)²+(a+b)²](a²-b²)18.(a-2b+3c-1)(a-2b-3c+1)19.(p+2z)²-2(p+2z)(p+3z)+(p+3z)²20.(-mn+ab)²21.(3x-1/2y)²22.（-1/3m²n+3/4mn²)²23.已知(a-b)²=7,（a+b)²=13求a²+b²,ab的值.在8：30之前。
1.（5-3m)²=25-30m+9m^22.(-5ayz+1/5a²)²=25a^2y^2z^2-2*5ayz*1/5a^2+1/25a^4=25a^2y^2z^2-2a^3yz+1/25a^43.(a+b)²(a-b)²(a²+b²)²=[(a^2-b^2)]^2(a^2+b^2)^2=(a^4-b^4)^2=a^8-2a^4b^4+b^84.（a-b-c)²=[a-(b+c)]^2=a^2-2a(b+c)+(b+c)^2=a^2-2ab-2ac+b^2+2bc+c^25.(2a+3b-4c)²=4a^2+4a(3b-4c)+(3b-4c)^2=4a^2+12ab-16ac+9b^2-24bc+16c^26.(a+b+c+d)(a+b-c-d)=[(a+b)+(c+d)][(a+b)-(c+d)]=(a+b)^2-(c+d)^2=a^2+2ab+b^2-c^2-2cd-d^27.(a+b+c+d)²=(a+b)^2+2(a+b)(c+d)+(c+d)^2=a^2+2ab+b^2+2ac+2ad+2bc+2bd+c^2+2cd+d^28.(x+y)(x-y)=x^2-y^29.(3x+2y)(3x-2y)=9x^2-4y^210.(-3x+2y)(-3x-2y)=9x^2-4y^211.(7mn²-8cd²)(7mn^2+8cd²)=49m^2n^4-64c^2d^412.1/5(30a²+15b²)(6a²-3b²)=1/5*5(6a^2+3b^2)(6a^2-3b^2)=36a^4-9b^413.(x+2y-3)(x-2y+3)=[x+(2y-3)][x-(2y-3)]=x^2-(2y-3)^2=x^2-4y^2+12y-914.(x+1/x)²-(x-1/x)²=(x+1/x+x-1/x)(x+1/x-x+1/x)=2x*2/x=415.(2a-b)²-2b²=4a^2-4ab+b^2-2b^2=4a^2-4ab-b^216.(5m+3n)²-(2m-n)²=(5m+3n+2m-n)(5m+3n-2m+n)=(7m+2n)(3m+4n)17.[(a+b)²+(a+b)²](a²-b²)=2(a+b)^2(a+b)(a-b)=2(a+b)^3(a-b)18.(a-2b+3c-1)(a-2b-3c+1)=[(a-2b)+(3c-1)][(a-2b)-(3c-1)]=(a-2b)^2-(3c-1)^2=a^2-4ab+4b^2-9c^2+6c-119.(p+2z)²-2(p+2z)(p+3z)+(p+3z)²=[(p+2z)-(p+3z)]^2=(-z)^2=z^20.(-mn+ab)²=m^2n^2-2mnab+a^2b^221.(3x-1/2y)²=9x^2-3xy+1/4y^222.（-1/3m²n+3/4mn²)²=1/9m^4n^2-2*1/3m^2n*3/4mn^2+9/16m^2n^4=1/9m^4n^2-1/2m^3n^3+9/16m^2n^423.已知(a-b)²=7,（a+b)²=13求a²+b²,ab的值.a^2-2ab+b^2=7.[1]a^2+2ab+b^2=13.[2][1]+[2]:2(a^2+b^2)=20a^2+b^2=10[2]-[1]:4ab=6ab=3/2.好累啊!