let the first integer be n
the second is (n+1), the third (n+2)
4n = (n+2) + 13
4n = n + 15
3n = 15
n = 5
4 x 5 = 20 = 7 + 13
the 3 integers are 5, 6, 7
did you try dividing? no.. as you clearly tried nothing
5x2+10x−15=(x+5)5x−(15x+15)−(15x+15)=−15(x+5)+605x2+10x−15=(15x−15)(x+5)+60The remainder is 60
we can add the two equations to obtain
2x2+(a+c)x+(b+d)=0x2+a+c2x+b+d2=0
Now just apply the quadratic formular1,2=−a+c2±√(a+c2)2−2(b+d)2
we can clean this up a bitr1,2=14(±√(a+c)2−8(b+d)−a−c)
If there is only a single shared root r1=r2if there are no shared roots(a+c)2−8(b+d)<0
Px + 40 = Qx + 20
Px +20 = Qx
20 = Qx - Px = (Q-P)x
If Q=P then (Q-P)x = 0 for all x and thus the original equation has no solutions.
I'm only seeing 3 triplets of integers that meet the specifications
(1, 3, 8), (1, 4, 5), (2, 2, 4)
Thus the sum asked for is
8 + 5 + 4 = 17
you got the first one right
for (b)
3x = 15
divide both sides by 3 to get
x=5
for (c)
x = 12-8 = 4
Px−37=Qx−37Px=QxP=Q leads to infinitely many solutionsP≠Q leads to the single solution x=0
x4−11x3+24x2=x2(x2−11x+24)(4x2−44x+96)=4(x2−11x+24)x4−11x3+24x2−(4x2−44x+96)=(x2−11x+24)(x2−4)=(x−8)(x−3)(x−2)(x+2)and thus the solutions are x=8, 3, 2, −2
ever think that B might be female?
These angles need to sum to 360 degrees.
120 + 80 + B = 360
B = 160 degrees