Question

(x-4)²(3x+4)²y²= 6y+9(√21-3)²(√5+2)²(1+√3)²(7+√2)²

Answer 1

Решения и ответы на фотографии

Answer 2

To solve for 'y' in the equation:

(x - 4)²(3x + 4)²y² = 6y + 9(√21 - 3)²(√5 + 2)²(1 + √3)²(7 + √2)²

You can start by simplifying the equation. Let's first simplify the right side of the equation:

6y + 9(√21 - 3)²(√5 + 2)²(1 + √3)²(7 + √2)²

Now, calculate the values inside the parentheses and the squares:

6y + 9(21 - 6√21 + 9)(5 + 4√5 + 4)(1 + 3 + 2√3)(7 + 2√2 + 2√14 + 2)

6y + 9(30 - 6√21)(9)(1 + 2√3)(9 + 2√2 + 2√14)

Now, continue to simplify:

6y + 2430 - 486√21)(1 + 2√3)(9 + 2√2 + 2√14)

Now, distribute the factors and simplify:

6y + 2430(1 + 2√3)(9 + 2√2 + 2√14) - 486√21(1 + 2√3)(9 + 2√2 + 2√14)

Now, distribute the terms within the parentheses:

6y + 2430(9 + 18√3 + 18 + 18√6 + 18√42 + 36√3) - 486√21(9 + 18√3 + 18 + 18√6 + 18√42 + 36√3)

Now, multiply the constants:

6y + 21870 + 43740√3 + 43740 + 43740√6 + 43740√42 + 87480√3 - 43740√21 - 87480√63 - 87480√21 - 87480√42 - 174960√3

Now, combine like terms:

6y + 21870 - 87480√21 - 174960√63 - 43740√21 - 87480√42 - 43740√3

Now, we have simplified the right side of the equation:

6y + 21870 - 131220√21 - 174960√63 - 43740√3 - 87480√42

Now, we can set this equal to the left side of the equation:

(x - 4)²(3x + 4)²y² = 6y + 21870 - 131220√21 - 174960√63 - 43740√3 - 87480√42

This is a quadratic equation in 'y', and to solve for 'y', you can set it equal to zero and use the quadratic formula:

(x - 4)²(3x + 4)²y² - 6y - 21870 + 131220√21 + 174960√63 + 43740√3 + 87480√42 = 0

Now, you can use the quadratic formula:

y = [ -b ± √(b² - 4ac) ] / (2a)

In this case, 'a' is the coefficient of y², 'b' is the coefficient of y, and 'c' is the constant term.

a = (x - 4)²(3x + 4)² b = -6 c = -21870 + 131220√21 + 174960√63 + 43740√3 + 87480√42

Now, you can plug these values into the quadratic formula to find the solutions for 'y'.