2012²-2013×2012 Using square difference formula and complete square formula to solve the problem,

2012²-2013×2012 Using square difference formula and complete square formula to solve the problem,

Original formula = 2012 × 2012-2013 × 2012
=2012×（2012-2013）
=2012×（-1）
=-2012
2012²-2013×2012
=2012²-(2012+1)×2012
=2012²-（2012²+2012）
=2012²-2012²-2012
=-2012
=（2012+1）（2012-1）-2013×2012
=2013×2011-2013×2012
=-2012
Find the square of (4x + 2Y), where 2x + y = 1
Find the square of (4x + 2Y), where 2x + y = 1
The square of (4x + 2Y)
= [2(2x+y) ] ²
= ( 2 x 1 )²
=2 ²
= 4
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"Choose as satisfactory answer"
Given x ^ & # 179; + x ^ & # 178; + X + 1 = 0, find 1 + X + x ^ & # 178; + x ^ & # 179; + x ^ 4 + ··· + x ^ 2012
X ^ & # 179; + x ^ & # 178; + X + 1 = (x ^ & # 178; + 1) (x + 1) = 0, so x = - 1, so 1 + X + x ^ & # 178; + x ^ & # 179; + x ^ 4 + ··· + x ^ 2012 = 1-1 + 1-1 + 1-1 · + 1 = 1
Because X & # 179; + X & # 178; + X + 1 = 0 ｜ X & # 179; + X & # 178; + x = - 1, X (X & # 178; + X + 1) = - 1 * 1, ｜ x = - 1
∴1+x+x^²+x^³+x^4+···+x^2012=1-1+1-…… -1 + 1 = 1 what does: - 1 * 1 mean?
Solve (4x squared - y squared) [(2x + y) squared - (2x-y) squared]
The original formula = (4x & # 178; - Y & # 178;) [(2x + y + 2x-y) (2x + y-2x + y)]
=(4x²-y²)[(4x)(2y)]
=8xy(4x²-y²)
=32x³y-8xy³
Given x + 1 / x = √ 5, then x & # 178; + 1 / X & # 178; = (?), X-1 / x = (?)
Because x + 1 / x = √ 5, X & # 178; + 1 / X & # 178; + 2x (1 / x) = 5 is reduced to X & # 178; + 1 / X & # 178; + 2 = 5, so x & # 178; + 1 / X & # 178; = 3 (x-1 / x) (x-1 / x) = x & # 178; + 1 / X & # 178; - 2 is obtained from the above formula, so (x-1 / x) = ± 1
x+1/x=√5
Square on both sides
x²+2+1/x²=5
x²+1/x²=3
(x-1/x)²
=x²-2+1/x²
=3-2
=1
So X-1 / x = ± 1 question: Thank you, the answer is very detailed. I have another problem: when a ≤ 1, then √ (1-A) &# = (?)
How to solve that square plus 4x equals zero
x²+4x=0
x(x+4)=0
x1=0 x2=-4
How much is x equal to 55? How much is x equal to 313
The third question: the square of x equals 476, how much is x equal to
Who can help to solve these three questions? I have to use them tonight. Thank you
First question x = 55 / x = 55 / X
Question 2 x = 313 / x = 313 / X
Question 3 x = 476 / x = 476 / X
The result of three questions can't be calculated by integers, so we can only use fractions
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X = 2 √ 119 x = 2 times root 119
1. x=±√55 2.x=±√313 3.x=±√476
Find the maximum value of - 4x ^ 2 + 16x-7 and what is x equal to when getting the maximum value
The original formula can be reduced to - 4 (X-2) ^ 2 + 11, so the maximum value of 11 is taken when x = 2
-4x^2+16x-7
=-4(X²-4X)-7
=-4(X²-4X+4)+16-7
=-4(X-2)²+9
≥9
When x = 2, the maximum value of - 4x ^ 2 + 16x-7 is 9
Given sina-3cosa = 0, find the value of 2 / 3sin ^ 2A + 1 / 4cos ^ 2
tana=3
2/3sin^2a+1/4cos^2
=[2/3sin^2a+1/4cos^2]/(sin²a+cos²a)
The numerator and denominator are divided by cos & # 178; a
=[4/3tana+1/4]/[tan²a+1]
=(4+1/4)/10
=17/4 *1/10
=17/40
When x is equal to, the square of negative x minus 4x plus 5 has the maximum value. What is the maximum value