One number is equal to the square of another. Find the numbers if both are positive and their sum is 756?

Answer 1

x^2 + x = 756

x(x+1) = 756

The square root of 756 would fall between x and x+1. sqrt(756) = about 27.5.

So, x=27.

Checking the result:

x = 27
x^2 = 729

x + x^2 = 27 + 729 = 756

That was a bit of a short-cut, which only works because the number in question is very close to a perfect square. If, instead of x(x+1) it was something like (x+3)(2x-8), you'd probably want to solve it rigorously:

x^2 + x = 756
x^2 + x - 756 = 0

Using the quadratic equation:

x = (-1 +/- sqrt(1^2 - 4*1*(-756))) / 2
x = (-1 +/- sqrt(3025)) / 2
x = (-1 +/- 55) / 2

The solutions to the quadratic are -56/2 (-28) and 54/2 (27). The negative solution can be discarded because the problem states that the number is positive.

Thus, x=27.

Answer 2

So first you put it in to an equasion. That comes out to be x^2 + x = 756
now complete the square. That comes out to be x^2+x+(1/4)=756 and 1/4
Then factor x^2+x+(1/4) to get (x+1/2)^2.
Then square root both sides to get x+1/2=27 and 1/2
Then subtract 1/2 from both sides to get x=27
So if x equals 27 then the square of that is 729 and those are your answers

Answer 3

27.
27^2=729, 27_729=756

Answer 4

y=x^2
y+x=756

x^2+x=756

x^2+x-756=0

Use quadratic formula

x= [-1±sqrt(1+4*756)]/2
= [-1±sqrt(3025)]/2
=[-1±55]/2
=-28,27
Discard -28 as we are talking about positive numbers

x=27
y=x^2=729

Check: 27+729= 756

The numbers are 27 and 729

Answer 5

x= (y^2)
x+y=756
(y^2)+y-756=0 solve this second degree equation by calculator or by formula y= ( -b(+or-)root(b^2- 4AC))/2a
so y=27 and x=756-27=729

Answer 6

y = x^2
x + y = 756

Then x + x^2 = 756
(x + 0.5)^2 = 756 + 0.25
(x + 0.5)^2 = 756.25
x + 0.5 = 27.5
x = 27, Hence y = 729

Answer 7

Use substitution to solve.

x + y = 765
x = √y