Question

Sum of a number and square roots of that number is 90 ,find the number​

Answer 1

Answer:

The sum of a positive integer and its square is 90. What is the number?

Step-by-step explanation:

Explanation:

Let n be the integer in question. Then we have

n2+n=90

⇒n2+n−90=0

We now have a quadratic equation to solve. We could use the quadratic formula, however we know that n is an integer, so instead let's try to solve by factoring instead.

n2+n−90=0

⇒n2+10n−9n−90=0

⇒n(n+10)−9(n+10)=0

⇒(n−9)(n+10)=0

⇒n−9=0orn+10=0

⇒n=9orn=−10

As it is given that n>0, we can disregard the possibility that n=−10, leaving us with our final answer of n=9

Checking our result, we find that it satisfies the given conditions:

9+92=9+81=90