Math Is Fun Forum

When we put x=1,
3x² + x = 3(1² ) + 1 = 4
Therefore,
4y² + y - 4 = 0
y = [-1 ± √ (1 + 64)]/8 = [-1 ± √ 65 ]/8
which is an irational number.
We see that here too x-y is not the square of a natural number

Two candles A and B, of equal height but different circumferences, burn for 4 hours and 3 hours respectively. If the two are lit at the same time, after what time would one candle be half the height of the other?

We are discussing this 2.500 years ahead of mankind
Maybe in 4,500 AD, brain and the body could be digitized,
maybe then the DNA pattern would be
010100101011100101011001011100011010100010110001.........................
and not
AGCTGGCTAACGTTACTGTTACACGTACGGAATCAGTTAAGCTAAGCT..........

Atoms were considered to be the building blocks, then the subatomic particles were discovered....and now, it is said that the subatomic particles like neutrons, protons, electorns etc are made up of quarks;
but I am not sure whether that is true for neutrinos, mesons, muons, positrons etc.

An eye for an eye, a tooth for a tooth....
Extrapolated,
a life for a life
It takes the society nowhere.
But what do we do with criminals involved in
Homicide / Terrorism / Drug trafficking / Adultery / Molesting ?
Forgive them?
Award a lesser sentence like life imprisonment??
Banish them ???

Hi Shelly,
There are 909 registered users in this forum.

The binomial expansion of the Left Hand Side
contains two terms, among many, which are
a^a*n and b^a*n which appear to make the LHS greater than the RHS,
but when we assign arbitrary values,
say a=10, b=1,000,000,000 and n=100
the LHS is (1,000,000,010)^1000, which would contain 9,001 digits;
the RHS becomes
100 x (100^1,000,000,000) which would contain more than 2 billion digits!
This happened because we assumed b>>n.
Otherwise, the LHS may be greater.
Say, when a=10, b=100, n=1000.
LHS would be 110^10,000 containing 20,414 digits and the RHS would be much smaller, viz. 100*(1000^100), containing approximately 300 digits!

Solving the two equations, you get
x = -5/2, y = -1/6
Hence, the two lines cross at
(-5/2, -1/6)

How the two equations are solved:-
First equation can be written as                x+3y = -3
The second equation can be written as     x - 3y = -2
Adding the two, we get                           2x = -5, or x = -5/2
Substituting this value in equation (1)     -5/2 + 3y = -3
                                                                       3y = -3 + 5/2
                                                                       3y = -1/2
                                                                         y = -1/6

I got killed when I was riding a bike, and I was shot at a short range with a pistol in the head

The world record holder remembers 100,000 places

Thanks, Mathsisfun,
I am on the verge of post # 200
and this an occassion for me to celebrate,
I shall take a big chunk of thhat