Math Is Fun Forum

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Two Equations Having One Solution

Hello,

Find the condition or conditions that the constants A, B, C, D, E, F need to satisfy so that the following two equations have one solution only:
y = A*x^2 + B*x + C
y = D*x^2 + E*x + F

Good luck,
Kerim

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Two Equations Having One Solution

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Two Equations Having One Solution

Bob

Your answer is right, but this is half the journey only.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Two Equations Having One Solution

?? It's the condition, so what more are you expecting?  Did you want the single solution too? It wasn't asked for was it?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Two Equations Having One Solution

?? It's the condition, so what more are you expecting?  Did you want the single solution too? It wasn't asked for was it?

Bob

Sorry for not being clearer.
I meant there are more conditions, if satisfied; the two equations will have one solution too.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Two Equations Having One Solution

For instance, When I read this exercise many decades ago, the question was:

Prove that the two equations have one solution if the following two conditions are satisfied:

B*D = E*A
and
A*E^2 - D*B^2 = 4*A*D*(F-C)

As you know, this is simply a special case.
Your answer is right always. I mean, your condition is satisfied in this case too.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.