Question

Y^2-12y+32=0 По теореме Виета

Answer 1

8 и 4
8*4=32
8+4=12
ВОТ И ВСЕ РЕШЕНИЕ

Answer 2

Solving the Equation using Vieta's Theorem

To solve the equation Y^2 - 12Y + 32 = 0 using Vieta's theorem, we can consider the quadratic equation in the form ax^2 + bx + c = 0. In this case, a = 1, b = -12, and c = 32.

According to Vieta's theorem, the sum of the roots of a quadratic equation is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. In other words, the sum of the roots is -b/a.

Similarly, the product of the roots is equal to the constant term divided by the coefficient of the quadratic term. In other words, the product of the roots is c/a.

For the equation Y^2 - 12Y + 32 = 0, the sum of the roots is -(-12)/1 = 12 and the product of the roots is 32/1 = 32.

Therefore, the roots of the equation can be found by solving the equation Y^2 - 12Y + 32 = 0 using the sum and product of the roots.

Let's find the roots using this information.

Finding the Roots

To find the roots of the equation Y^2 - 12Y + 32 = 0, we can use the quadratic formula:

Y = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values a = 1, b = -12, and c = 32 into the quadratic formula, we get:

Y = (-(-12) ± √((-12)^2 - 4(1)(32))) / (2(1))

Simplifying further:

Y = (12 ± √(144 - 128)) / 2

Y = (12 ± √16) / 2

Y = (12 ± 4) / 2

This gives us two possible values for Y:

Y1 = (12 + 4) / 2 = 16 / 2 = 8

Y2 = (12 - 4) / 2 = 8 / 2 = 4

Therefore, the roots of the equation Y^2 - 12Y + 32 = 0 are Y = 8 and Y = 4.

Conclusion

Using Vieta's theorem, we found that the roots of the equation Y^2 - 12Y + 32 = 0 are Y = 8 and Y = 4.