Question

Two number which product is 1800 and sum is -110

Answer 1

Answer:

Our two equations are:

x+y=16

xy=55

Rewriting equation (1) in terms of just y= something, we get:

y=16−x

Substituting this into equation (2) leaves us:

x(16−x)=55

16x−x2=55⟹x=5 or 11

which can be easily seen by factoring or using the quadratic formula. It follows that y=11|x=5 and y=5|x=11.

Thus your solutions in terms of (x,y) are (5,11) and (11,5).

Answer 2

Let the two numbers be x and y.

A.T.Q. X*Y = 1800 ----- (I)

X+Y = -110 ------ (II)

Now let's square the second equation.

$X^2+Y^2+2XY= (-110)^2$ = 12100

$X^2+Y^2+2 XY = 12100$

Now, lets subtract 4XY from both sides, this will make the question easier. ;)

$(X^2+Y^2+2XY)-4XY=12100-4(XY)$

$X^2+Y^2-2XY = 12100- 4(1800)$  (Because XY = 1800 (given) )

$(X-Y)^2=4900$

$X-Y=\sqrt{4900}$

X-Y = $\frac{+}{-}$70 ---- (III)

And we were given, in equation (II)

X + Y=-110.

Solving (II) and (III),

X = -20, -90

Y= -90, -20