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Mathematics problems in grade eight It is known that a + B = 10, ab = 17 Find the value of A-B
(a+b)²=10²
a²+2ab+b²=100
ab=17
So a & sup2; + B & sup2; = 100-2 × 17 = 66
(a-b)²=a²-2ab+b²=66-2×17=32
So A-B = - 4 √ 2 or A-B = 4 √ 2
Solution of quadratic equation with one variable`
solve equations
1. The square of | x | + 3 | x | - 4 = 0
Let | x | = y, we know that y ≥ 0, then the deformation of the equation is as follows:
y^2+3y-4=0
(y-1)(y+4)=0
The solution is y = 1, y = - 4 (negative, rounding off);
therefore
|x|=1
Then x = ± 1
So the original equation has two real roots 1 and - 1
Bottleneck in solving quadratic equation with one variable?
1 -- equation: 4 / A & # 178; + 9 / A & # 178; - 16 = 1, find a & # 178;
2 -- equation: 3 / B & # 178; + 5 / B & # 178; + 16 = 1, find B & # 178;
How to solve, explain white point, why to solve so, thank you
:4/a²+9/a²-16=1
13 / A & # 178; = 1 + 16 (add with denominator)
13 / A & # 178; = 17 (equivalent to 13 △ A & # 178; = 17)
a²=13÷17
a²=13/17
3/b²+5/b²+16=1
8/b²=-15
b²=8÷（-15）
b²=-8/15
The square of (4Y-2) is equal to?
According to the formula (a-b) &# 178; = (a-b) * (a-b) = A & # 178; - 2Ab + B & # 178;, it can be obtained that,
（4y-2）²= 16y²-16y+4
The common factor of 2x ^ 2-8y ^ 2, x ^ 2-4xy + 4Y ^ 2
2x^2-8y^2
=2(x^2-4y^2)
=2(x+2y)(x-2y)
x^2-4xy+4y^2
=(x-2y)^2
So it's x-2y
X-2y + 3 = 0 find x ^ 2 - (4Y + 1) x + 4Y ^ 2 + 8y
x-2y=-3
The formula is wrong
Original formula = x & sup2; - 4xy-4x + 4Y & sup2; + 8y
=(x-2y)²-4(x-2y)
=9+12
=21
4xy - (square of x-square of 4Y)
4xy-(x²-4y²)=-(x²-4xy+4y²)=-(x-y)²
Square of 1-x + square of 4xy-4y=
Square of 1-x + square of 4xy-4y = 1 - (x-2y) ^ 2 = (1-x + 2Y) (1 + x-2y)
-The power of X + the power of 4xy-4y
The second power of (a + b) - 12 (a + b) + 36
I'm always confused,
-The power of X + the power of 4xy-4y
=-(x-y)^2
The second power of (a + b) - 12 (a + b) + 36
=(a+b-6)^2
If the square of X + the square of 4Y = 4xy, then the value of (x + 2Y) / (X-Y) is_______________ .
The known formula is x ^ 2-4xy + 4Y ^ 2 = 0
(x-2y)^2=0
So x = 2Y
The original formula is 4
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