Question

X^2-7x+m-2=0;x1=a-1;x2=a+2 найдите m=?​

Answer 1

Ответ:а²+а

Объяснение:

По теореме Виета  х1×х2=m-2

m-2=(а-1)(а+2)

m=(а-1)(а+2)+2

 m=а²+2а-а-2+2

m=а²+а

Answer 2

To find the value of $m$, we can use the given quadratic equation and the given roots. Let's substitute $x_1 = a-1$ and $x_2 = a+2$ into the quadratic equation $x^2 - 7x + m - 2 = 0$ and solve for $m$.

Substituting $x_1 = a-1$ into the equation: $(a-1)^2 - 7(a-1) + m - 2 = 0$

Expanding and simplifying: $a^2 - 2a + 1 - 7a + 7 + m - 2 = 0$ $a^2 - 9a + m + 6 = 0$ ----(1)

Substituting $x_2 = a+2$ into the equation: $(a+2)^2 - 7(a+2) + m - 2 = 0$

Expanding and simplifying: $a^2 + 4a + 4 - 7a - 14 + m - 2 = 0$ $a^2 - 3a - 12 + m = 0$ ----(2)

Since both equations (1) and (2) represent the same quadratic equation, their coefficients must be equal. Comparing the coefficients, we have:

For $a^2$ term: 1 = 1 For $a$ term: -9 = -3 For constant term: m + 6 = -12

From the second equation, we get $m + 6 = -12$, so by solving for $m$: $m = -12 - 6$ $m = -18$

Therefore, the value of $m$ is -18.