Mathematics
Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.
Quadratic Equations
54 Likes
Answer
Let two parts be x and (20 - x).
According to question,
3x2 - (20 - x) = 10
3x2 + x - 20 = 10
3x2 + x - 30 = 0
3x2 + 10x - 9x - 30 = 0
x(3x + 10) - 3(3x + 10) = 0
(x - 3)(3x + 10) = 0
x - 3 = 0 or (3x + 10) = 0
x = 3 or x = .
20 - x = 20 - 3 = 17.
Hence, numbers are 3 and 17.
Answered By
17 Likes
Related Questions
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers.
Find two consecutive positive odd numbers, the sum of whose squares is 74.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60.
Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers.
Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.