Question

5х(х-3)квадраты-5(х-1)квадраты+15(х+2)(х-2)=

Answer 1

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Answer 2

5x(x-3)² - 5(x-1)² + 15(x+2)(x-2) = 5x(x²-6x+9) - 5(x²-2x+1) + 15(x²-4) = 

5x³-30x²+45x - 5x²+10x-5 + 15x² -60 = 5x³ - 20x² + 55x - 65

Answer 3

To solve this equation, we will first simplify the left-hand side by expanding the squares:

5х(х-3)² - 5(х-1)² + 15(х+2)(х-2)

= 5х(х² - 6х + 9) - 5(х² - 2х + 1) + 15(х² - 4)

= 5х³ - 30х² + 45х - 5х² + 10х - 5 + 15х² - 60

= 5х³ - 10х² + 70х - 65

Now we have simplified the equation to a cubic polynomial. To solve for x, we can try to factor the polynomial or use numerical methods like the cubic formula or Newton's method.

Unfortunately, this polynomial does not appear to factor easily, so we will use numerical methods to find its roots. Using the cubic formula, we get:

x = (-b ± √(b² - 4ac - 3b³) ) / 3a

where a = 5, b = -10, and c = 70-65 = 5.

Plugging in these values, we get:

x = (-(-10) ± √((-10)² - 4(5)(5) - 3(-10)³)) / (2*5)

x = (10 ± √(100 - 100 - 300)) / 10

x = (10 ± √(-300)) / 10

x = (10 ± 10√(-3)) / 10

x = 1 ± √3 i

Therefore, the solutions to the equation are x = 1 + √3 i and x = 1 - √3 i, where i is the imaginary unit.