Forwarded from Questions collection (Yogesh)
3^9(1+27+729+3^n-9)
3^9(757+3^n-9)
3^9 is perfect cube
Have to make (757+3^n-9) cube
Next cube 10^3 it could be
1000-757=243
So 3^n-9=3^5
N=9+5=14
3^9(757+3^n-9)
3^9 is perfect cube
Have to make (757+3^n-9) cube
Next cube 10^3 it could be
1000-757=243
So 3^n-9=3^5
N=9+5=14
Forwarded from Questions collection (Yogesh)
Y^2+y-2=0 quadratic
Maximum infinity
Minimum -(1+8)/4=-9/4
X^2+1 can't be 0.
Y can't be infinity
Y--- maximum
When x^2+1 minimum =1 at x=0
Y=2(0)/1=0 maximum y
So [-9/4,0]
Maximum infinity
Minimum -(1+8)/4=-9/4
X^2+1 can't be 0.
Y can't be infinity
Y--- maximum
When x^2+1 minimum =1 at x=0
Y=2(0)/1=0 maximum y
So [-9/4,0]
Forwarded from Shubham Kumar
Cos@ + sin& =1/3
Sin@ + sin&= 1/4
Squaring and adding
Cos(@-&)= -263/288
2cosยฒ(@-&)/2 -1 = -263/288
Cos(@-&)/2= 5/24
So
Tan(@-&)/2=โ551/5
Sin@ + sin&= 1/4
Squaring and adding
Cos(@-&)= -263/288
2cosยฒ(@-&)/2 -1 = -263/288
Cos(@-&)/2= 5/24
So
Tan(@-&)/2=โ551/5
Forwarded from Math World (Azizakhon Turakhujaeva)
Deleted Account
Photo
root(x)=a, root(y)=b
a^3+b^3=19
a^2b+ab^2=15
ab(a+b)=15
(a+b)((a+b)^2-3ab)=19
(a+b)^3-3โข15=19
(a+b)^3=64
a+b=4
ab=15/4
(4-b)โขb=15/4
4b^2-16b+15=0
b=2.5; b=1.5
a=1.5; a=2.5
x+y=(1.5)^2+(2.5)^2=8.5 โ โ
a^3+b^3=19
a^2b+ab^2=15
ab(a+b)=15
(a+b)((a+b)^2-3ab)=19
(a+b)^3-3โข15=19
(a+b)^3=64
a+b=4
ab=15/4
(4-b)โขb=15/4
4b^2-16b+15=0
b=2.5; b=1.5
a=1.5; a=2.5
x+y=(1.5)^2+(2.5)^2=8.5 โ โ
Forwarded from Deleted Account
x=root(5)+1; y=root(5)-1
x/y=(5+1+2sqrt5)/(5-1)=(3+sqrt5)/2
y/x=(5+1-2sqrt5)/(5-1)=(3-sqrt5)/2
(x/y)^2+(y/x)^2+4(x/y+y/x)+6=
(9+5+6sqrt5)/4+(9+5-6sqrt5)/4+4*3+
+6=
7+12+6=25 โ โ
x/y=(5+1+2sqrt5)/(5-1)=(3+sqrt5)/2
y/x=(5+1-2sqrt5)/(5-1)=(3-sqrt5)/2
(x/y)^2+(y/x)^2+4(x/y+y/x)+6=
(9+5+6sqrt5)/4+(9+5-6sqrt5)/4+4*3+
+6=
7+12+6=25 โ โ
Monk
Solve it
cos(A+B)=24/25 -> sin(A+B)=7/25
sin(A-B)=15/17 -> cos(A-B)=8/17
tan(A+B)=7/24
tan(A-B)=15/8
tan(2A)=(7/24+15/8)/(1-7/24*15/8)=
(8โข7+15โข24)/(24โข8-7โข15)=416/87
sin(A-B)=15/17 -> cos(A-B)=8/17
tan(A+B)=7/24
tan(A-B)=15/8
tan(2A)=(7/24+15/8)/(1-7/24*15/8)=
(8โข7+15โข24)/(24โข8-7โข15)=416/87