The sum of two integers is 69. the greater integer is three more than two times the other. what is the greater integer?

1 answer:

7 0

the sum of three consecutive odd integers is 69. Find the integers.
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1st: 2x-1
2nd: 2x+1
3rd: 2x+3
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Equation:2x-1 + 2x+1 + 2x+3 = 69
6x + 3 = 69
2x + 1 = 23
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So 2x-1 = 21
And 2x+3 = 25

let:
x be the first odd integer
x + 2 be the 2nd odd integer
x + 4 be the 3rd odd integer
solution:
1st odd integer + 2nd odd integer + 3rd odd integer = 69
x + (x+2) + (x+4)= 69

3x + 6 = 69
3x = 69 - 6
3x = 63 (dividing both sides by three)
x = 21
_______________________________________
x=21
x+2=23
x+4=25
therefore, the 1st integer is 21, the 2nd is 23 and the 3rd is 25..

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Two or zero expresses the possible number of positive real solutions for the given polynomial equation.

Answer: Option D

Step-by-step explanation:

Given equation:

$x^{3}-4 x^{2}-7 x+28=0$

First, we put hit and trial method to find out the one solution. So, if we put x=4 then the above expression will become zero. We can also write the above expression as

$(x-4) \times\left(x^{2}-7\right)=0$