The sum of squares of two positive integer is 208 if the square of the larger number is 18times the smaller number find the number.&atwo digit number is 4 times the sum of its digit and twice the product of its digitfind the number.which smallest irrational number should be added 4+root5 to get a rational number.
Answers
Answered by
1
I will answer the first part of the question on the sum of squares of two positive integers.
Let the integers be x and y. Then, from the question we can deduct that
x^2 + y^2 = 208 and
x^2 = 18*y or 18y
Substituting the value of x^2 in the first equation, we get
18y + y^2 = 208.
Rearranging the equation, we get
y^2 + 18y - 208 = 0.
This is a quadratic equation. Thus, the solution is given by
y = (-b ± sqrt(b^2-4ac))/2awhere b = 18, a = 1 and c = -208.
Thus, we get
y = (-18 ± sqrt (18^2 - 4 x 1 x -208))/2 * 1
y = (-18 ± sqrt (324 + 872))/2 = (-18 ± sqrt 1156)/2
y = (-18 ± 34) / 2
Since the integers are positive, we need not consider -34. Considering 34, we get
y = (-18 + 34)/2 = 16 / 2 = 8.
Substituting the value of y = 8 in the second equation, x^2 = 18y, we get
x^2 = 18 x 8 = 144 or x = sqrt (144) or ±12.
Since the integers are positive, the number is 12. Thus, the numbers are 12 and 8.
Let the integers be x and y. Then, from the question we can deduct that
x^2 + y^2 = 208 and
x^2 = 18*y or 18y
Substituting the value of x^2 in the first equation, we get
18y + y^2 = 208.
Rearranging the equation, we get
y^2 + 18y - 208 = 0.
This is a quadratic equation. Thus, the solution is given by
y = (-b ± sqrt(b^2-4ac))/2awhere b = 18, a = 1 and c = -208.
Thus, we get
y = (-18 ± sqrt (18^2 - 4 x 1 x -208))/2 * 1
y = (-18 ± sqrt (324 + 872))/2 = (-18 ± sqrt 1156)/2
y = (-18 ± 34) / 2
Since the integers are positive, we need not consider -34. Considering 34, we get
y = (-18 + 34)/2 = 16 / 2 = 8.
Substituting the value of y = 8 in the second equation, x^2 = 18y, we get
x^2 = 18 x 8 = 144 or x = sqrt (144) or ±12.
Since the integers are positive, the number is 12. Thus, the numbers are 12 and 8.
Similar questions
Social Sciences,
8 months ago
Hindi,
8 months ago
Chemistry,
8 months ago
Physics,
1 year ago
Business Studies,
1 year ago