2x-5y + 8 = 3x + Y-5 for XY Absolute value of 2x-5y + 8 + 3x + Y-5 radical = 0 Finding real numbers x and Y

2x-5y + 8 = 3x + Y-5 for XY Absolute value of 2x-5y + 8 + 3x + Y-5 radical = 0 Finding real numbers x and Y

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Let X and y be positive real numbers, and 2x + 5Y = 20, and find the maximum value of the XY power of 2

20=2x+5y≥2√(2x*5y)
square
400≥40xy
xy≤10
SO 2 ^ (XY) ≤ 2 ^ 10
So the maximum is 1024

Factorization factor 2x minus y minus XY minus x minus 5Y minus 6

This problem is solved by the method of undetermined coefficient
Because 2x & sup2; - xy-y & sup2; = (2x + y) (X-Y)
So let 2x & sup2; - xy-y & sup2; - x-5y-6 = (2x + y + a) (X-Y + b)
=2x²-xy-y²+ax-ay+2bx+by+ab
=2x²-xy-y²+(a+2b)x+(b-a)y+ab
The comparison coefficient is a + 2B = - 1, B-A = - 5, ab = - 6
The solution is a = 3, B = - 2
So 2x & sup2; - xy-y & sup2; - x-5y-6 = (2x + y + 3) (x-y-2)

4 (x + 2) = 1-5y 3 (y + 2) = 3-2x find XY

x=-3
y=1
xy=-3

-x^5y-xy+2x^3y

Do you want to decompose factors?
If so, then
-x^5y-xy+2x^3y
＝-xy(x^4-2x²+1)
=-xy(x²-1)²
=-xy(x+1)²(x-1)²

The solution of 2x square-y square-xy-x-5y-6rt

=(2x+y)(x-y)-2(2x+y)+3(x-y)-6
=(2x+y+3)(x-y-2)

It is known that a, B and C are trilateral of △ ABC and satisfy (A & # 178; - B & # 178;) (A & # 178; + B & # 178; - C & # 178;) = 0,
Then its shape is______ Triangle Pythagorean theorem! No root sign!

(a) (a-t-178; (a-b-\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\forisosceles triangle or right triangle

Given the factorization of the polynomial 2x ^ 3-x ^ 2-3x + K, there is a factorization of 2x + 1, and the value of K is obtained

Let the quotient of 2x ^ 3-x ^ 2-3x + K divided by 2x + 1 be a
Then 2x ^ 3-x ^ 2-3x + k = a (2x + 1)
X = - 1 / 2,2x + 1 = 0, so the right side equals 0
Then when x = - 1 / 2, the left side is also equal to 0
SO 2 * (- 1 / 8) - 1 / 4-3 * (- 1 / 2) + k = 0
k=-1

It is known that the polynomial 2x ^ 4-x ^ 3 + 3x ^ 2-1 has a factor 2x + 1 and another factor is

2x^4-x^3+3x^2-1
=2x^4+x^3-2x³-x²+4x^2-1
=x³(2x+1)-x²(2x+1)+(2x+1)(2x-1)
=(2x+1)(x³-x³+2x-1)
The other factor is X & # 179; - X & # 178; + 2x-1

If X-1 is a factor of the polynomial 2x ^ 2-3x + N, then n=____ .

Method 1: calculate by undetermined coefficient method: let x = 1, X-1 = 0, that is, 2x ^ 2-3x + n = 0, 2 × 1-3 × 1 + n = 0, n = 1. Method 2: since the highest degree of X is quadratic, let the factorization of 2x ^ 2-3x + n be (x-1) (AX + b) (x-1) (AX + b) = ax ^ 2 - (a-b) X-B = 2x ^ 2-3x + N, then a = 2, A-B = 3, n = - B, so n = 1