It is known that m and N are two of the equations x? - 2x-1 = 0, and (7m? - 14m + a) (3N? - 6n-7) = 8, the value of a is equal to

It is known that m and N are two of the equations x? - 2x-1 = 0, and (7m? - 14m + a) (3N? - 6n-7) = 8, the value of a is equal to

x^2-2x-1=0
7x^2-14x-7=0
3x^2-6x-3=0
(7+a)(3-7)=8
(7+a)*(-4)=8
7+a=-2
a=-9

If M and N are two of the equations x2-2x-1 = 0 and (7m2-14m + a) (3n2-6n-7) = 8, then the value of a is equal to______ .

∵ m and N are two of the equations x2-2x-1 = 0,
∴m2-2m=1，n2-2n=1①，
∵ the original formula = (7m2-14m + a) (3n2-6n-7) = 8, namely [7 (m2-2m) + a] [3 (n2-2n) - 7] = 8,
Substituting ① into (7 + a) (3-7) = 8, a = - 9
So the answer is: - 9

Let m, n be two of the equations x-2x-1 = 0, and (7m-14m + a) (3n-6n-7) = 8, find the value of A

According to the meaning of the title, m-2m-1 = 0; therefore, 7 (m-2m-1) = 0, that is, 7m-14m-7 = 0; similarly, 3n-6n-3 = 0, ﹥ 7m-14m + a) (3n-6n-7) = (7m-14m-7 + 7 + a) (3n-6n-3-4) = (7 + a) × (- 4) = 8 ﹥ a = - 9

If the solution of equation 2x + 1 = 3 and equation 2x-a = 0 are the same, then a=______ .

From 2x + 1 = 3, 2x = 2,
The solution is x = 1,
Substituting x = 1 into the equation 2x-a = 0 leads to 2-A = 0,
∴a=2．

The two equations of X 1-2x = 3 and 0.5 (1-2ax) = x + a have the same solution. Find the value of A

1-2x = 3 x = - 1 into equation 2
0.5 (1 + 2a) = A-1 0.5 + A-A = - 1 is wrong

If the equation a ^ 2x ^ 2 + (2a + 3) y ^ 2 + 2aX + A + 1 = 0 is a circle, then the value of real number a is equal to The correct answer is - 1. How to calculate it?

It is obvious that if the equation is a circle, then a? = 2A + 3A? - 2a-3 = 0 (A-3) (a + 1) = 0A = - 1 or a = 3 because - a > 0

Let the real coefficient equation 2x ^ 2 + 3ax + A ^ 2-2a = 0 have the modulus of at least one root equal to 2, and find the value of real number a

i. The equation has two real roots
△=9a^2-8(a^2-2a)=a^2+16a≥0 => a≤-16 or a≥0
If the equation has a root x 0 = 2, then 8 + 6A + A ^ 2-2a = 0, then a has no real number solution
If the equation has root x0 = - 2, then 8-6a + A ^ 2-2a = 0, and the solution is a = 4 + 2 √ 2 or a = 4-2 √ 2
II. The equation has a pair of conjugate imaginary roots with module 2
△=9a^2-8(a^2-2a)=a^2+16a -16

If a is a root of equation x ^ 2-2x + 1 equal to 0, find the value of - A + 2A + 2oo8

A=1
-1+2+2008=2009

It is known that x = 2 is a quadratic equation of one variable If 2x2-2a = 0, then the value of 2a-1 is______ .

Put x = 2 into equation 3
2x2-2a = 0, 6-2a = 0, a = 3
Then: 2a-1 = 2 × 3-1 = 5

If a is a root of the equation x squared + 2x-1 = 0, then the value of 2A squared + 4a-1 is equal to To process

solution
A is the root of the equation x 2 + 2x-1 = 0
Put x = a into the equation
Then a 2 + 2a-1 = 0
∴a²+2a=1
Qi
2a²+4a-1
=2(a²+2a)-1
=2×1-1
=1