2m=a+b
2n=b+c
b^2=ac
a/m+c/n=(an+cm)/mn=[a(b+c)/2+c(a+b)/2]/mn
=2(ab+ac+ac+bc)/(a+b)(b+c)
=2(ab+2b^2+bc)/(ab+2b^2+bc)
=2
2. (a+b-c)(a+b+c)=a
[(a+b)-c][(a+b)+c]=ab
Square difference formula in (a+b)*(a-b)=a squared-b squared
Taking (a+b) as a whole
So [(a+b)^2]-c^2=ab
a^2+b^2+ab=c^2
So a^2+b^2-c^2=-ab
So cosC=(a^2+b^2-c^2)/2ab
= (-ab )/2ab
=-1/2
So, angle C=120 degrees
3.
From the known x=[6*8‰*a*(1+8)^6]/[1+8‰]^6-1],
The 8% at the back means eight thousandths of a degree, and the symbols have to go to the word to copy them, which is troublesome
y=[12* 8%*a*(1+8%)^12]/[(1+8%)^12-1],
So x/y=[(1+8%)^6+1]/2*(1+8%)^6 <1
So x<y
4.
Let the first term be a
S5=a(1+q+q^2+q^3 +q^4)=2
S10=a(1+q+q^2+q^3+q^4)+aq^5(1+q+q^2+q^3+q^4)
=a(1+q^5)(1+q+q^2+q^3+q^4)=6
S10÷S5=1+q^5=3
q^5=2
a16+a17+a18+a19+a20
=aq^15(1+q+q^2+q^3+q^4)
=(q^5)^3×a(1+q+q^2+q^3+q^4)
=2^3×2
=16
5. (Write 0.5 in place of the expression one-half)
y=x^2+ax+1=(x+a/2)^2-a^2/4+1>=0
Axis of symmetry x=-a/2
If -a/2>0.5
a<-1,the domain of definition is on the left side of the axis of symmetry, and it is a subtractive function
So x=0.5, y min= 1.25+0.5a>=0
a>=-0.25,does not match a<-1
0<=-a/2<=0.5
-1<=a<=0,in the domain of definition of the axis of symmetry
x=-a/2,y min=-a^2/4+1>= 0
-2<=a<=2
Then -1<=a<=0
So a minimum=-1