Equation x / 2 × 4 + X / 4 × 6 + X / 6 × 8 + +Root X of X / 2012 × 2014=

Equation x / 2 × 4 + X / 4 × 6 + X / 6 × 8 + +Root X of X / 2012 × 2014=

What's on the right side of the equation? If it's 1, then x = 2014 / 503

For the equation (1 + k) x & # 178; + (1 + k) y & # 178; + 4 (k-1) x + 2 (2k-1) y + 4-8k = 0, take any two values of K1 and K2 which are not equal to - 1, whether the curve corresponding to the equation is a circle? If not, explain the reason

Note: for example, x ^ 2 + y ^ 2 + DX + ey + F = 0
That is, (X-D / 2) ^ 2 + (y-e / 2) ^ 2 = [D ^ 2 + e ^ 2-4f] / 4
When radius r = [D ^ 2 + e ^ 2-4f] / 4 > 0
Then x ^ 2 + y ^ 2 + DX + ey + F = 0 is a circle; otherwise, it is not a circle}
∵k1、k2≠-1 ∴k1+1、k2+1≠0
So x ^ 2 + y ^ 2 + [4 (k-1) x] / (K + 1) + [(4k-2) y] / (K + 1) + (4-8k) / (K + 1) = 0
When {[4 (k-1) / (K + 1)] ^ 2 + [(4k-2) / (K + 1)] ^ 2-4 (4-8k) / (K + 1)} / 4 > 0
Then the curve corresponding to the equation is a circle
The solution is left to the owner
Note: for reference only!

When k is sum value, the equation x & # 178; + 2 (k-1) x + K & # 178; + 2k-4 = 0,1 has two unequal real roots
2. There are no real roots 3. There are two equal real roots

Equation x & # 178; + 2 (k-1) x + K & # 178; + 2k-4 = 0
Δ=4(k-1)²-4(k²+2k-4)
=4(5-4k)
(1)
When Δ > 0, that is 5-4k > 0, K