Given x ^ 2-4x + 4Y ^ 2-4y + 5 = 0, find the value of (x ^ 2 + y ^ 2) (x ^ 2-y ^ 2) - (x + y) ^ 2 (X-Y) ^ 2? | Math enthusiast | Mathematical art

Given x ^ 2-4x + 4Y ^ 2-4y + 5 = 0, find the value of (x ^ 2 + y ^ 2) (x ^ 2-y ^ 2) - (x + y) ^ 2 (X-Y) ^ 2?

X ^ 2-4x + 4Y ^ 2-4y + 5 = 0 (x ^ 2-4x + 4) + (4Y ^ 2-4y + 1) = 0 (X-2) ^ 2 + (2y-1) ^ 2 = 0 X-2 = 02y-1 = 0 x = 2Y = 1 / 2 original formula = x ^ 4-y ^ 4 - [(x + y) (X-Y)] ^ 2 = x ^ 4-y ^ 4 - (x ^ 2-y ^ 2) ^ 2 = x ^ 4-y ^ 4 + 2x ^ 2Y ^ 2-y ^ 4 = 2 * 4 * 1 / 4-2 * 1 / 16 = 15 / 8

RELATED INFORMATIONS

1. Given 4x ^ 2 + 4x + 3 = y ^ 2 + 4Y. Find the value of X-Y
2. Given y = 2-x, find the value of 4x + 4y-3
3. 4 (square of x) + square of Y -- 4x -- 4Y + 5 = 0, X / Y -- y / x =?
4. X square - 2XY + y square + 4x-4y + 4 Factoring it
5. Solve the system of equations x (x + 1) (3x + 4Y) = 144 x square + 4x + 4Y = 24
6. How to solve this system of equations with the square of X + the square of y-4x + 4y-1 = 0 and 3x-4y-4 = 0
7. Solve the equations {4x + 8 (x + y) = 480,4y + 9 (x + y) = 480
8. How to solve the equation system x square + 4x + 4Y square = 9; X square + xy = 0
9. If the solution of the equations 4x + y = K + 1x + 4Y = 3 satisfies the condition 0 < x + y < 1, then the value range of K is () A. -4＜k＜1B. -4＜k＜0C. 0＜k＜9D. k＞-4
10. 1 / 2xy-4x square, y square + 4Y square - x cube arranged by X ascending power is?
11. Given the circle x square + y square + 25 = 0, find the tangent equation of the point (4, - 3)
12. Tangent equation of a point m (4, - 3) over circle x square + y square = 25
13. The tangent equation of over current M (3,4) and square of circle x + square of y = 25
14. The tangent equation of a circle passing through the square of X + the square of y = 25 (- 3,4) is
15. Given that the circle x2 + Y2 + 2x-4y + 1 = 0 is symmetric with respect to the line 2aX by + 2 = 0 (a > 0, b > 0), then the minimum value of 4A + 1b is () A. 4B. 6C. 8D. 9
16. Comparison of the size of N + 1 power of N and (n + 1) power of n
17. The size relation between N + 1 of N and N + 1 power of n From n = 1,2,3,4 Start with these simple numbers and summarize the rules
18. What is the law of the relationship between the power of N + 1 and the power of (n + 1) What are the rules
19. The relationship between the power of N + 1 of N and the power of (n + 1) is
20. The relation between the N + 1 power of N and the n power of (n + 1)