What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
It’s 2 if I did my math right because I did it 2 tones and both of the times I got 2
Answer:
2over/a -b-c
Step-by-step explanation:
remove the parentheses
Answer:
x = 7
Step-by-step explanation:
8x = 56
To solve this, we must simplify. To do this, we must divide each side by 8. This, in term, will give us the value of x.
8x = 56
---- ----
8 8
56/8 = 7
x = 7
Our answer is x = 7
Answer:
2 , 1\2
Step-by-step explanation:
b² - 4ac = (-5)² - 4*2*2
= 25 - 16
= 9
![x= \dfrac{-[-5] + 3}{2*2} ; x = \dfrac{-[-5]-3}{2*2}\\\\x =\dfrac{5+3}{4} ; x = \dfrac{5-3}{4}\\\\x=\dfrac{8}{4} ;x = \dfrac{2}{4}\\x = 2 ; x = \dfrac{1}{2}](https://tex.z-dn.net/?f=x%3D%20%5Cdfrac%7B-%5B-5%5D%20%2B%203%7D%7B2%2A2%7D%20%3B%20%20x%20%3D%20%5Cdfrac%7B-%5B-5%5D-3%7D%7B2%2A2%7D%5C%5C%5C%5Cx%20%3D%5Cdfrac%7B5%2B3%7D%7B4%7D%20%3B%20x%20%3D%20%5Cdfrac%7B5-3%7D%7B4%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B8%7D%7B4%7D%20%20%3Bx%20%3D%20%5Cdfrac%7B2%7D%7B4%7D%5C%5Cx%20%3D%202%20%3B%20x%20%3D%20%5Cdfrac%7B1%7D%7B2%7D)
