(x³y - y²) (x³y + y²); x = -1, y = -2
Answers
Answer:
y=2x
Substitute into other equation
x2−(2x)2=3
x2−(4x2)=3
x4x2−4x2=3
x4−4x2=3
x4−4=3x2
x4−3x2−4=0
Substitute. Let p=x2
Thus,
x4−3x2−4=0
becomes…
p2−3p−4=0
Simple Quadratic, factor..
(p−4)(p+1)=0
Substitute back in for p
(x2−4)(x2+1)=0
x2−4=0
x2=+4
x=2orx=−2
Find y
xy=2
y=2x
y=2−2=−1or y=22=1
Next, find x3+y3and x3−y3.
Answer is -9, -7, 7, and 9.
What is the value of x³+y³, when x+y=10 and x²+y²=60?
What's x³+y³ if x³-y³=9,x-y=3?
How does (x³+y³) become=(x+y) (x²-xy+y²)?
If x= (√3-√2) / (√3+√2) and y= (√3+√2) / (√3-√2) then how do you find the value of x²+xy+y²?
How do you factorize x⁴ + x²y² + y⁴?
As given,
x²−y²=3 (i)
xy=2 (ii)
Assuming x & y are real…
We can write,
x2+2ixy−y2=3+2×2i=(x+iy)2
Where , i=−1−−−√
Thus we can say,
(x+iy)2=3+4i
(x+iy)2=(4+2×2×i+(i)2)
(x+iy)2=(2+i)2
Thus ,
x+iy=±(2+i)
Which implies that,
Either,
x= 2 & y= 1
Or,
x= -2 & y= -1
Both these cases satisfy the initial conditions!
Thus
x3+y3=9or−9
And,
x3−y3=7or−7
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So we know that
x2−y2=3
Multiply this by x2 and you’ll get
x4−x2y2=3x2
But we also know that xy=2 so we have
x4–3x2–4=0
Make the following variable change
x2=u+32
and replace it (where you find leave) to get after a few simplifications that
u2−254=0
So what you’ve got is that
u=±52
=x2−32
Hence −1 and 4 are the only possible values for x2. Thus x∈{±i,±2} (where i is the imaginary unit).
Now, back to y, we find that
(x,y)∈{(2,1),(−2,−1),(i,−2i),(−i,2i)}
Thence, you can certainly calculate x3±y3.
x2−y2=3….(1)
xy=2………..(2)
Multiplying (1) by 2 and subtracting 3 times (2) from it,
2x2–3xy−2y2=0………..(3)
this gives (2x+y)(x-2y)=0
Case I
2x+y=0 ; y=-2x ; Substituting in (2) x2=−1 ; x=±i
y=∓2i .we get (i,-2i), (-i,2i)
Case II
x=2y ;that gives y2=1 ; y=±1 ; x=±2
So (2,1) and (–2,-1) are the solutions.
These values can be used for further calculations.
What number is equivalent to 3⁴/ 3²?
How do you simplify: y³ × y³ + y² × y⁴?
If x³-x²-x=3³-3²-3, what's x?
What is the value of 3√7?
If (x+y) = 12 and xy= 20, what is the value of x⁴+y⁴?
xy =2 implies that y = 2/x
x^2 - (2/x)^2 = 3
x^2 - 4/(x^2) = 3
x^4 - 4 = 3x^2
x^4 - 3x^2 - 4 = 0
(x^2 - 4)(x^2 + 1) = 0
(x + 2)(x-2)(x^2 + 1) = 0
x = +/-2, which means y = 2/(+/-2) = +/- 1
or Complex number solution
x = +/- i, where i = sqrt (-1), which means
y = 2/(+/-i) = 2 i / (+/-(i^2)) = 2i/(-/+1) = -/+2 i
(x,y) = (2, 1), (-2, -1), (i, -2i), (-i, 2i)
x^3 + y^3 = (2^3) + (1^3) = 7
or = (-2)^3 + (-1)^3 = -7
x^3 - y^3 = (2^3) - (1^3) = 7
or (-2)^3 - (-1)^3 = -7
So x^3 + y^3 = +/- 7 depending on values of (x,y)
x^3 - y^3 = +/-7 depending on values of (x,y)
or x^3 + y^3 = (i^3) + (-2i)^3 = i^3 -8(i^3) = - 7i^3
=
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X^2 - y^2 = 3
x y = 2
Y= 2/x
X^2-(2/x)^2 = 3
X^2–4/x^2 = 3
=> X^4 - 4 = 3x^2
=> X^4 - 3x^2 - 4 = 0
=> (X^2 - 4)(X^2 +1) = 0=> x^2 = 4 or x^2 = -1
X=√(-1) is complex so skip to x^2 = 4
X = 2 or X = -2
Y = 2/x => y =1 or y = -1
X^3 + y^3 = 2^3 + 1^3 = 8+1 = 9
X^3 - y^3 = 2^3 - 1^3 = 8–1 =7
X^3+y^3 = -8–1 = -9,
= -8+1 = -7
X^3 + - y^3 = 9, 7, -9, -7
X^2 – y^2 = 3; xy = 2
y = (2/x); x^2 – (x/2)^2 = 3
x^2 – (x^2)/4 = ¾ x^2 = 3
x^2 = (4/3)(3) = 4
x = ± 2; y = ± 1
note x and y must have the same sign
x^3 = ± 8; y^3 = ±1
x^3 ± y^3 can be (-8 -1); (-8 +1); (+8 -1); (+8 +1)
or -9; -7, +7; +9
x^2–y^2=3
xy=2➛y=2/x
x^2-(2/x)^2=3
x^2–(4/x^2)=3
x^4–4=3x^2
(x^2–1)(x^2+4)=0
x=±1
x=1➛y=2
x=-1➛y=-2
You work out the rest.
by trial
X=2
Y=-1
X3 +Y3=8–1 =7
Try 2 and 1, surprise 2x1=2 so x=2&y=1, 2^3+1^3=8+1=9 and 8–1=7
Pretty sure this is right. Please comment if anything is wrong.
x=2 , y=1
x^2 - y^2= 4–1=3
so :
8+1=9
8–1=7
What is the value of x³+y³, when x+y=10 and x²+y²=60?
What's x³+y³ if x³-y³=9,x-y=3?
How does (x³+y³) become=(x+y) (x²-xy+y²)?
If x= (√3-√2) / (√3+√2) and y= (√3+√2) / (√3-√2) then how do you find the value of x²+xy+y²?
How do you factorize x⁴ + x²y² + y⁴?
What number is equivalent to 3⁴/ 3²?
How do you simplify: y³ × y³ + y² × y⁴?
If x³-x²-x=3³-3²-3, what's x?
What is the value of 3√7?
If (x+y) = 12 and xy= 20, what is the value of x⁴+y⁴?
What is x²-x³ equal to?
If x+y = 3 √8 , x-y = √2 , then the value of 8xy (x²+y²) is?
How do you solve (x²-1)²= (x³-1)²?
How can I expand and simplify this (x³ + y²) ²?
If x² +2 = 2x, then what is the value of x⁴–x³ +x²+2?
Step-by-step explanation:
Hope this will help