It is known that x1x2 is two real roots of the square - 6x + k = 0 of the univariate quadratic equation x, and the square of X1 and the square of X2 - x1x2 = 115 (1) Find the value of K (2) find the square of X1 + the square of x2 + 8

It is known that x1x2 is two real roots of the square - 6x + k = 0 of the univariate quadratic equation x, and the square of X1 and the square of X2 - x1x2 = 115 (1) Find the value of K (2) find the square of X1 + the square of x2 + 8

x ²- 6x+k=0△=（-6） ²- 4K ≥ 0, K ≤ 9 with real root. X1 + x2 = 6x1x2 = kx1 ² x2 ²- x1x2=115k ²- k=115,k ²- k-115=0k={1±√[(-1) ²- 4 * 1 * (- 115)]} / 2K1 = (1 + √ 461) / 2 (rounded) K2 = (1 - √ 461) / 2x1 ²+ x2&s...

It is known that x1x2 is the two real roots of the univariate quadratic equation x ^ 2-6x + k = 0, and X1 ^ 2 is multiplied by x2 ^ 2-x1-x2 = 115. Find the value of K and find the value of X1 ^ 2 + x2 ^ 2 + 8

(1)x1+x2=6 ,x1x2=k
x1^2x2^2-x1-x2=(x1x2)^2-(x1+x2)=k^2-6=115
K ^ 2 = 121, i.e. k = ± 11
∵ x1, X2 are two real roots of the equation x ^ 2-6x + k = 0 about X, ∵ △ > 0
When k = 11, △ = B ^ 2-4ac = (- 6) ^ 2-4 × one × 11=-8＜0
∴k=-11
(2)x1^2+x2^2+8=(x1+x2)^2-2x1x2+8=6^2-2 × (-11)+8=66

What is the sum of X1 and X2, and what is the multiplication of X1 and X2

x1+x2=-(b/a)

X1 * x2 =? Is X1 * x2 = C / a (C / a) in the univariate quadratic equation

Uh, yes

What is the product of two roots and what is the sum of two roots in solving a quadratic equation of one variable? (in letters) If you don't know any data in the univariate quadratic equation AX2 + BX = C, let you use a B C to represent the sum product of the two roots X1 x2 solved. This seems to be called the Vita theorem.. forget

It's called Veda's theorem
ax ²+ bx+c=0
x1=[-b-√(b ²- 4ac)]/2a
x2=[-b+√(b ²- 4ac)]/2a
x1+x2=[-b-√(b ²- 4ac)-b+√(b ²- 4ac)]/2a=-2b/2a=-b/a
x1x2=[-b-√(b ²- 4ac)][-b+√(b ²- 4ac)]/(4a ²)
=[(-b) ²- (b ²- 4ac)]/(4a ²)
=4ac/(4a ²)
=c/a
So X1 + x2 = - B / A
x1x2=c/a

What is delta equal to? (solving quadratic equation of one variable)

5x square + 4x + 2 = 0, a = 5, B = 4, C = 2, △ = b square - 4ac