Hi i have to complete a dimond where its 9 on top and 2 bottom if tried all numbers . What are the 2 numbers that add to 2 but when multiplied is 9
"What are the 2 numbers that add to 2 but when multiplied is 9 ?"
let them be x and y
x+y=2 ----> y = 2-x
xy = 9
x(2-x) = 9
2x - x^2 - 9 = 0
x^2 - 2x + 9 = 0
This quadratic equation has no real solution ...
x = (2 ± √(4-4(1)(9)) )/2
= (2 ± √-32)/2 = (2 ± 4√2)/2
= 1 ± 2√-2
= 1 ± 2i , <----- these are both complex numbers, but they work for your condition stated.
sum: 1+2√2 i + 1-2√2 i = 2
product: (1+2√2 i)(1-2√2 i) = 1 - 2√2 i + 2√2 i - 8i^2 , but i^2 = -1
= 1 + 8 = 9
I don't have the foggiest idea what "complete a dimond where its 9 on top and 2 bottom if tried all numbers " means.
Not familiar with that type of English.
near the middle , should have been:
= 1 ± 2√2 i , <----- these are both complex numbers ....
To find the two numbers that add up to 2 and multiply to 9, you can use a trial and error method. Start by listing all the possible pairs of numbers that multiply to 9: (1, 9), (3, 3), and (9, 1).
Now, check if any of these pairs adds up to 2:
1 + 9 = 10 (not equal to 2)
3 + 3 = 6 (not equal to 2)
9 + 1 = 10 (not equal to 2)
None of the pairs satisfies the condition. In this case, there are no two numbers that add up to 2 and multiply to 9.