Determine all positve integer a such that the equation \(2x^2-210x+a=0\) has two prime roots, i.e. both roots are prime numbers
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Determine all positve integer a such that the equation \(2x^2-210x+a=0\) has two prime roots, i.e. both roots are prime numbers
Phương trình: \(2x^2-105x+a=0\Leftrightarrow x^2-105x+\frac{a}{2}=0\)không thể có nghiệm kép được vì 105 là số lẻ
Giả sử phương trình này có 2 nghiệm là b, c ta có
\(\hept{\begin{cases}2b^2-210b+a=0\left(1\right)\\2c^2-210c+a=0\left(2\right)\end{cases}}\)
Lấy (1) - (2) vế theo vế ta được
\(2b^2-210b-2c^2+210c=0\)
\(\Leftrightarrow\left(b-c\right)\left(b+c-105\right)=0\)
\(\Rightarrow b+c-105=0\Leftrightarrow b+c=105\)
\(\Rightarrow\)Một trong 2 số b hoặc c phải là số chẵn
Giả sử số chẵn đó là c thì ta có c = 2 ( vì c nguyên tố)
\(\Rightarrow b=103\)
Từ đây ta có:\(x^2-105x+\frac{a}{2}=\left(x-2\right)\left(x+103\right)=x^2-105x+206\)
\(\Rightarrow a=2.206=412\)
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Let a,b be the roots of equation \(x^2-px+q=0\) and let c,d be the roots of the equation \(x^2-rx+s=0\), where p,q,r,s are some positive real numbers. Suppose that :
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}\)
is an integer. Determine a,b,c,d .
Let a,b be the roots of equation \(x^2-px+q=0\) and let c,d be the roots of the equation \(x^2-rx+s=0\), where p,q,r,s are some positive real numbers. Suppose that :
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}\)
is an integer. Determine a,b,c,d .
Ta có:
\(\hept{\begin{cases}ab=q\\a+b=p\end{cases}}\)và \(\hept{\begin{cases}cd=s\\c+d=r\end{cases}}\)
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}=\frac{2\left(qc+sb+sa+qd\right)}{p^2+q^2+r^2+s^2}\)
\(=\frac{2\left(qr+sp\right)}{p^2+q^2+r^2+s^2}\le\frac{2\left(qr+sp\right)}{2\left(qr+sp\right)}=1\)
Với M = 1 thì \(\hept{\begin{cases}q=r\\p=s\end{cases}}\)
Tới đây thì không biết đi sao nữa :D
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thôi bỏ bài này đi cũng được vì chưa tới lúc cần dung phương trình
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It is known that the roots of the equation \(3x^5+9x^4-6x^2+5x-7=0\)are all integers.How many distinct roots does the equation have
how many different prime numbers a's are there such that a+20 and a+40 are also prime numbers
If \(a=2\): \(a+20=22\)is not a prime number.
If \(a=3\): \(a+20=23\), \(a+40=43\)are both prime numbers.
If \(a>3\), we have \(a=3k+1\)or \(a=3k+2\).
- \(a=3k+1\Rightarrow a+20=3k+21⋮3\)is not a prime number.
- \(a=3k+2\Rightarrow a+40=3k+42⋮3\)is not a prime number.
Question 1:K is a prime number and a multiple of 43. What is K?Answer: K Question 2:How many prime numbers are less than 10? Answer: There are numbers.Question 3:The smallest factor of 82 is Question 4:The smallest multiple of 47 is Question 5:In the following figure, RQ 12cm and PR 17cm. PQ cm Question 6:In the following figure, AN 5cm and AB 8cm. NB cm Question 7:A prime number between 42 and 46 is Question 8:Find the sum of all the factors of 19Answer: Question 9:The sum of two of fol...
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Question 1:
K is a prime number and a multiple of 43. What is K?
Answer: K =
Question 2:
How many prime numbers are less than 10?
Answer: There are numbers.
Question 3:
The smallest factor of 82 is
Question 4:
The smallest multiple of 47 is
Question 5:
In the following figure, RQ = 12cm and PR = 17cm. PQ = cm
Question 6:
In the following figure, AN = 5cm and AB = 8cm. NB = cm
Question 7:
A prime number between 42 and 46 is
Question 8:
Find the sum of all the factors of 19
Answer:
Question 9:
The sum of two of following numbers is divisible by 4 and 6.
What are the two numbers?
(Write numbers in order, beginning smaller and use “;”)
Answer:
Question 10:
How many prime numbers have formed ?
Answer: There are numbers
Cái gì cũng phải vùa thôi chứ. Hix. Cả 1 lèo.
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Cau 1:1,25
Cau:Tit
Cau:Tit
Cau:Tit
Cau:Tit
Cau:Tit
Cau:Cau:Tit
Tit
Cau:Tit
Cau:Tit
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đòi hỏi vừa thôi đi thi toán chứ có phải thi hỏi đâu mà hỏi 1 lèo thế hỏi thế mình giải hết đc cx ko trả lời
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Question 1:The smallest odd multiple of 9 is Question 2:K is a prime number and a multiple of 43. What is K?Answer: K Question 3:How many prime numbers are less than 10? Answer: There are numbers.Question 4:P is a prime number and a factor of 8. What is P?Answer: P Question 5:A prime number between 42 and 46 is Question 6:In the following numbers, which has the most factors?Answer: Question 7:The number 55 has factors.Question 8:Find the sum of all the factors of 15Answer: Question 9:How man...
Đọc tiếp
Question 1:
The smallest odd multiple of 9 is
Question 2:
K is a prime number and a multiple of 43. What is K?
Answer: K =
Question 3:
How many prime numbers are less than 10?
Answer: There are numbers.
Question 4:
P is a prime number and a factor of 8. What is P?
Answer: P =
Question 5:
A prime number between 42 and 46 is
Question 6:
In the following numbers, which has the most factors?
Answer:
Question 7:
The number 55 has factors.
Question 8:
Find the sum of all the factors of 15
Answer:
Question 9:
How many times does the digit “0” appear in numbers from 1 to 1000?
Answer:
Question 10:
If m, n are consecutive odd numbers and is divisible by 3 and 5 then m =
day la toan ko phai tieng anh
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cái gì mà nhiều thế
toán chớ hông fai TA nhé mà kinh zậy
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Xem thêm câu trả lời
Find the sum of all prime numbers between 1 and 100 that are simultaneosly 1 greater than multiple of 4 and 1 less than a multiple of 5
Given that 511 is the sum of two prime numbers a and a<b. What is the value of a ?
- two prime numbers are: 2 and 509
So, the vale of a is: 2
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Ta có: a +b = 511 (là số nguyên tố)
Suy ra: a phải là 2 (số nhuên tố), và b phải là 509 (số nguyên tố)
Ví a<b, Nên ta chọn giá trị của a là 2
Đáp án: 2
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chinh xac! hai so do la 2 va 509 do ban!
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