Explain why n² +n - 10 = 0

Two numbers differ by 1 and have a product of 10. If n is the smallest number, explain why n²+n-10 = 0

The solution: a - n = 1 and an = 10 so (10/n) -n = 1 therefore n² +n -10 = 0

How do i even get to the solution?

if n is the smallest of 2 consecutive numbers which equal 10, then the product of n and n+1 is 10,
n(n+1)=10 ,
n²+n=10,
n²+n-10=0
that's the solution it's looking for, no actual numbers.

(edited 5 years ago)

Original post by OJ Emporium

Two numbers differ by 1

i.e.

x - y = 1

and have a product of 10.

i.e.

xy = 10

If n is the smallest number,

i.e.

n = y

So x = 1 + n
So xy = (1+n)n

OP

Original post by AngeryPenguin

i.e.

x - y = 1

i.e.

xy = 10

i.e.

n = y

So x = 1 + n
So xy = (1+n)n

Thank you for breaking these down into steps man, made it easier💯

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