Math Problems
#Problems #Quest26
#Solutions | #Quest26
RHS≥0=> 3≤x≤6
Simplify:
1+(x-6)(x-8) = (x-7)^2
4-(x-11)(7-x)=(x-9)^2
25-(x+1)(9-x)=(x-4)^2
If x≥4, 2x-8=9x-18-x² => x=5,2 => x=5
If x<4, 8-2x=9x-18-x² =>(11-√17)/2.
Only solutions: 5 and (11-√17)/2.
Author:@Azaradichta
RHS≥0=> 3≤x≤6
Simplify:
1+(x-6)(x-8) = (x-7)^2
4-(x-11)(7-x)=(x-9)^2
25-(x+1)(9-x)=(x-4)^2
If x≥4, 2x-8=9x-18-x² => x=5,2 => x=5
If x<4, 8-2x=9x-18-x² =>(11-√17)/2.
Only solutions: 5 and (11-√17)/2.
Author:
Math Problems
#Problems #Quest20
#Solutions | #Quest20
p+q+r=3p
pq+qr+pr=3q²
pqr=r³
pq=r²
r²+qr+pr=3q²
r(r+q+p)=3q²
rp=q²
pq=r²
p²qr=q²r²
p²=qr
q²=rp
r²=pq
pq+pr+qr=3q²
pq+q²+qr=3q²
r²+qr-2q²=0
(r-q)(r+2q)=0
r≠-2q
r=q
p=q=r
Author:Anar
p+q+r=3p
pq+qr+pr=3q²
pqr=r³
pq=r²
r²+qr+pr=3q²
r(r+q+p)=3q²
rp=q²
pq=r²
p²qr=q²r²
p²=qr
q²=rp
r²=pq
pq+pr+qr=3q²
pq+q²+qr=3q²
r²+qr-2q²=0
(r-q)(r+2q)=0
r≠-2q
r=q
p=q=r
Author:
Math Problems
#Problems #Quest22
#Solutions | #Quest22
e^x=t
dt=e^xdx
1/(x-1)(x³-1)=1/(x-1)²(x²+x+1)=(x+1)/(3x²+3x+3) +(2-x)/3(x-1)²=(x+1)/3(x²+x+1) +1/3(x-1)²-1/3(x-1)
Author:Anar
e^x=t
dt=e^xdx
1/(x-1)(x³-1)=1/(x-1)²(x²+x+1)=(x+1)/(3x²+3x+3) +(2-x)/3(x-1)²=(x+1)/3(x²+x+1) +1/3(x-1)²-1/3(x-1)
Author:
Math Problems
#Problems #Quest1 (repost)
#Solutions | #Quest1
sum of the n first positive odds is n².
So just divide the sixth positive odd = 11, by the twenty-first positive odd = 41.
Answer: 11/41.
Author:@Sidneifs
sum of the n first positive odds is n².
So just divide the sixth positive odd = 11, by the twenty-first positive odd = 41.
Answer: 11/41.
Author: