If x + 5Y = 6, then x2 + 5xy + 30y=______ ．

If x + 5Y = 6, then x2 + 5xy + 30y=______ ．

The original formula = x (x + 5Y) + 30y = 6x + 30y = 6 (x + 5Y) = 6 × 6 = 36

Find the linear equation which is perpendicular to the straight line x-2y = 0 and tangent to the hyperbola C: 2x ^ 2-5y ^ 2 = 30

It is known that the slope of the straight line is k = - 2, so let the equation be y = - 2x + B. since the straight line is tangent to the hyperbola, there must be an intersection point between them. Therefore, by substituting the straight line equation into the hyperbola equation, we can get: 18x ^ 2-20bx + 5B ^ 2 + 30 = 0. From the upper decomposition, we can see that the equation has only one real solution, then ⊿ = 400B ^ 2-4 * 18 * (5b ^ 2 +...)

Given 2x + 5Y = 2, find the value of 2x2 + 5xy + 5Y

∵ 2x + 5Y = 2, ∵ 2x2 + 5xy + 5Y = x (2x + 5Y) + 5Y (3 points) = 2x + 5Y (4 points) = 2. (5 points)

Find the length of the common chord of square of circle x + square of y = 4 and square of circle x + square of y-4y-12 = 0

x²+y²=4
x²+y²-4y=12
subtract
4y=-8
y=-2
Put in the first one
x=0
So there's only one common point
In fact, the two gardens are inscribed
So there's no common string