If lgx + lgY = 1, then 5 / x + 2 / y is the minimum

If lgx + lgY = 1, then 5 / x + 2 / y is the minimum

lg(xy)=1
xy=10
5/x+2/y=(5y+2x)/xy=(5y+2x)/10
True number x > 0, Y > 0
5y+2x>=2√(5y*2x)=2√(10*10)=20
Take the equal sign when 5Y = 2x
Y = 2x / 5, xy = 10, with positive solutions
So we can get the equal sign
So the minimum value is 20 / 10 = 2

Given lgx + lgY = 1, the minimum value of 2 / x + 5 / y is?

Because lgx + lgY = 1, x, Y > 0
lgx+lgy=lg(xy)=lge
xy=e x=e/y
2 / x + 5 / y = 2Y / E + 5 / Y ≥ 2 radical [(2Y / E) (5 / y)] = 2 radical (10 / E)

Given that the tolerance of the arithmetic sequence {an} is - 2, and A2, A4, A5 are equal to the arithmetic sequence, then A2 is equal to______ ．

Because the tolerance of the arithmetic sequence {an} is - 2, and A2, A4, A5 are proportional, so A42 = a2a5, that is, (A2 − 4) 2 = A2 (A2 − 6)

It is known that the tolerance of the arithmetic sequence an is 2. If A2, A4 and A5 are in a proportional sequence, then the value of A2 is?

If A2, A4 and A5 are in equal proportion sequence, that is, A4 ^ 2 = A2 * A5
That is, (a1 + 3D) ^ 2 = (a1 + D) (a1 + 4D), d = 2
So (a1 + 6) ^ 2 = (a1 + 2) (a1 + 8)
a1^2+12a1+36=a1^2+10a1+16
2a1=-20
a1=-10
a2=a1+d=-10+2=-8