Ax + B = Bx + C Ax - Bx = (C - B) x (A - B) = (C - B) x = (C - B) / (A - B)
bx+cy=d bx=d-cy x=d-cy ----- b answer: d-cy ----- b
3a+ax+3b+bx = 3(a+b)+(a+b)x = (a+b)(3+x)
x2+bx+ax+ab = x2+ax+bx+ab = x(x+a)+b(x+a) = (x+a)(x+b)
Two: one is 0, the other is -b/a ax2 + bx + c = 0, but c = 0 ⇒ ax2 + bx + 0 = 0 ⇒ ax2 + bx = 0 ⇒ x(ax + b) = 0 ⇒ x = 0 or (ax + b) = 0 ⇒ x = -b/a
Ax + B = Bx + C Ax - Bx = (C - B) x (A - B) = (C - B) x = (C - B) / (A - B)
bx+cy=d bx=d-cy x=d-cy ----- b answer: d-cy ----- b
3a+ax+3b+bx = 3(a+b)+(a+b)x = (a+b)(3+x)
3x2 + bx - 5 = 0 ∴ 3x2 + bx = 5 ∴ x2 + bx/3 = 5/3 ∴ x2 + bx/3 + (b/6)2 = 5/3 + (b/6)2 ∴ (x + b/6)2 = (45 + b2) / 36 ∴ x + b/6 = ±[(45 + b2) / 36]1/2 ∴ x = [-b ± (45 + b2)1/2] / 6
x2+bx+ax+ab = x2+ax+bx+ab = x(x+a)+b(x+a) = (x+a)(x+b)
b(a-x)
10 is the value of b that would make X plus bx-24 factorisable.
Two: one is 0, the other is -b/a ax2 + bx + c = 0, but c = 0 ⇒ ax2 + bx + 0 = 0 ⇒ ax2 + bx = 0 ⇒ x(ax + b) = 0 ⇒ x = 0 or (ax + b) = 0 ⇒ x = -b/a
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(a - b)(x + y)
If x is a null matrix then Ax = Bx for any matrices A and B including when A not equal to B. So the proposition in the question is false and therefore cannot be proven.
A quadratic involving x and y is usually in the form 'y = ax2 + bx + c'. This form is y in terms of x, so we must rearrange it. y = ax2 + bx + c y/a = x2 + bx/a + c/a y/a = x2 + bx/a + d + e, where c/a = d + e, e = (b/a)2 y/a - e = x2 + bx/a + d y/a -e = (x + b/a)2 √(y/a - e) = x + b/a √(y/a - e) - b/a = x