Math, asked by beeridi8rdeebashree, 1 year ago

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 tejasmba
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.
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