What are 2 numbers that add up to 7 and multiply to be 5?

Answer 1

p+q=7 so p=7-q
pq=5

(7-q)q = 5

7q - q² = 5

q² - 7q + 5 = 0

let a=1, b=-7 and c=5

then

q = ½[7 ± √(7² - 4*1*5)]

q = ½[7 ± √(49 - 20)]

q = ½(7 ± √29)

So q = ½(7-√29) is one solution

p = 7-q = 7 - ½(7-√29)

p = ½(7 + √29)
p+q = ½(7 + √29) + ½(7-√29)
p+q = ½(7 + √29 + 7 - √29) = 7

So they add to 7

pq = ½(7 + √29) * ½(7 - √29)
pq = ¼(7 + √29)(7 - √29)
pq = ¼[49 + 7√29 - 7√29 - (√29)²]
pq = ¼[49 - 29] = 5


So the numbers 7 + √29 and 7 - √29 add to 7 and multiply to 5

Answer 2

If you call the numbers x andy, then x + y = 7 and xy = 5. You can rewrite the first equation as y = 7 - x. Then x * (7 - x) = 5. Multiply out the parentheses: 7x - x^2 = 5. Subtract 5 from each side, rearrange, and you get -x^2 + 7x - 5 = 0, which is a quadratic equation. You solve it by plugging the coefficients into the formula x = (-b +/- sqrt(b^2 - 4*a*c))/2a.

In this case, A, the coefficient of x^2, is -1. B, the coefficient of x, is 7, and C, the constant, is -5. So you have x = (-7 +/- sqrt(49 - 4*-1*-5))/2*-1. Simplify what's in the parentheses and you get x = (-7 +/- sqrt(29))/-2. To go any further, you'd have to use a calculator or a spreadsheet. I got 6.193 and 0.807. Those are the two numbers you're looking for.

Answer 3

Well, I tried to solve this, but I don't come up with an answer that makes sense:

x + y = 7
x*y = 5

y = 7-x

so x*y = x*(7-x) = 5

7x - x² = 5

or 0 = x² - 7x + 5

Solving the Quadratic Equation, I get the two roots as:

x = 6.1926 y = 0.8074

x + y = 6.1926 + 0.8074 = 7
x*y = 6.1926*0.8074 = 5

Answer 4

0.8074 and 6.1926.

Used the quadratic formula for hypothetical function x^2 +7 + 5 since I figure thats prolly why your asking as well.

Answer 5

none do. If you're doing factorising, then are you sure it's not 2x in one of the brackets. Because then (2x+5) (x+1) would work as the 2x would double the one for the addition bit and not affect it for the multiplication bit.

Answer 6

a+b = 7
a*b = 5
Now get your Algebra together and solve it. (Hint: These will not be 'nice' integer values ☺)

Doug

Answer 7

x+y= 7
x= 7-y

x y=5
so (7-y)y = 5
7y-y²=5

y² -7y= -5
y²-7y+5=0


y= [-b +-(√b² - 4 ac)] /2a

= [7 +-√(-7)² - 4(1)(5) ] /2

=( 7+-√49-20 ) /2

= 7+-5.385 /2

so y = 6.1925 or 0.8075

and x = 0.8075 0r 6.1925

so the 2 numbers are 0.8075 and 6.1925