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Given that a is equal to the root 3 minus 1, find the square of a plus 3A plus 5
A = √ 3-1, so a ^ 2 = 4-2 √ 3
So a ^ 2 + 3A + 5 = 4-2 √ 3 + 3 √ 3-3 + 5 = 6 + √ 3
Given that a is equal to 2 plus 1 / 3 of the root sign and B is equal to 2 minus 1 / 3 of the root sign, find the square of a plus the square of B plus 5ab minus 3A minus 3B
a=1 / 2+√3＝2－√3
b＝1 / 2－√3＝2＋√3
a^2+b^2+5ab-3a-3b=(a+b)^2+3ab-3(a+b)=16+3-12=7
Given that a real number a satisfies | 2004-A | root sign a-2005 = A. find the value of a-2004 square It is known that the real number a satisfies | 2004-A | + root sign a-2005 = a. Find the square value of a-2004
Because a-2005 is greater than or equal to 0, so a is greater than or equal to 2005. The original formula = a-2004 + root sign a-2005-a = 0 root sign a-2005-2004 = 0 root sign a-2005 = 2004 a-2005 = 2004 square a = 2004 square + 2005
If | 2004-A | + (Radix a-2005) = a, how to decompose the factor of a-2004 squared 1
2004-a|+√(a-2005)=a
Because (a-2005) > = 0
So a > = 2005
So the formula is converted into:
(a-2004)+√(a-2005)=a
a-2004+√(a-2005)=a
√(a-2005)=2004
a-2005=2004^2
a-2004^2=2005
If x, y are real numbers, and Y ＜ X-1 + 1-x + 1 / 2, simplify: 1 / 2 Y-1, 1-2y + y 2
y＜√(x-1) + √(1-x) + 1/2
x-1≥0,
1-x ≥ 0, that is, X-1 ≤ 0
∴x-1=0,x=1
∴y＜√(x-1) + √(1-x) + 1/2 = 1/2
∴1-y＞0
∴|1-y|/(y-1) = (1-y)/(y-1) = -1
There is a problem, first simplify in the evaluation (x + 2 / X-2 + x-4 / 4x) / - X-1 / 4, where x = - radical 3. When doing the problem, Xiao Ling wrongly copied "x = - root 3" into x = root 3, but his calculation result is the same as the correct answer. Why
((x-2)/(x+2)+4x/(x^2-4))÷1/(x^2-4)
=(x-2)/(x+2)∙(x^2-4)/1+4x/(x^2-4)∙(x^2-4)/1
=(x-2)^2+4x=x^2+4
Because - square root 3 square root 3 square root 3 square root sign 3
So the answer is the same
If 1 / 2 of the root term (X-2) is meaningful, simplify the root term [4-4x + (the square of x)]
Because 1 / 2 of the root (X-2) is meaningful and the root (X-2) is the denominator
So X-2
One problem is to simplify and then evaluate (x + 2 / X-2 + x-4 / 4x) divided by x-square-1 / 4, where x = - root sign 3, Xiaoming X = - root 3 is copied as x = root 3,
(x + 2 / 2 X-2 + x-4x) divided by xsquare-1 / 4
=(x 2 - 4x + 4 + 4x) × (x + 2) (X-2)
=x²＋4
X = radical 3
Original formula = 7
X = - radical 3
Original formula or = 7
Because here's x? No matter what sign precedes root 3, the result is the same
Reduce the absolute value of 2-x minus the square of root sign (x-4) to - 2, and find the value range of X
How can this have a range? It's clearly a value. X is equal to 2
If x and y are real numbers and satisfy the absolute value of (x-3) + the root sign (y + 3) = 0, then the value of the 2014 power of (x in Y) is?
The absolute value of (x-3) + root sign (y + 3) = 0
So, y = 0-3
x=3,y=-3
So x / y = - 1
So the original formula = (- 1) 2014 power = 1
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