Question

The result of adding 45 to a certain number is same as multiplied by 10 find the number

Answer 1

Answer:

Let’s start with the straightforward approach.

Let  a  and  b  be two numbers whose sum is  10  and whose product is  45 .

a+b=10

ab=45

Rearranging the first equation we get:

b=10−a

Now substituting  10−a  for  b  in the second equation:

a(10−a)=45

10a−a2=45

−a2+10a−45=0

Now we have a proper quadratic equation, and we can use the quadratic formula to solve for  a :

a=−10±102−4(−1)(−45)−−−−−−−−−−−−−−√2(−1)

a=−10±−80−−−−√−2

As you can see, we’re forced to deal with the square root of a negative number, which means our answers will be complex. Carrying on…

a=5–25–√i  and  a=5+25–√i

These are the possible values of  a . To solve for  b , just take  10−a . Easy, right?

Here’s another way to prove that there is no real-number solution to this problem. The chart below shows the product of  a  and  b  as a function of  a  for  0≤a≤10 .

As you can see, the product of  a  and  b  never gets close to  45 . Its maximum value is  25 , and that happens when  a=5 . QED.

I hope that'll helps