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.

Let larger number be x and smaller number be y, According to first part, x 2 + y 2 = 208 ........(i) x 2 = 18y ........(ii) Substituting value of x 2 from (ii) in (i) we get, ⇒ 18y + y 2 = 208 ⇒ y 2 + 18y - 208 = 0 ⇒ y 2 + 26y - 8y - 208 = 0 ⇒ y(y + 26) - 8(y + 26) = 0 ⇒ (y - 8)(y + 26) = 0 ⇒ y - 8 = 0 or y + 26 = 0 ⇒ y = 8 or y = -26. Since, numbers are positive integers, ∴ y ≠ -26. Substituting value of y = 8 in (ii), ⇒ x 2 = 18(8) = 144 ⇒ x = . Since, numbers are positive integers, ∴ x ≠ -12. Hence, numbers are 12 and 8.

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Mathematics

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.

Quadratic Equations

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Two integers differ by 2 and sum of their squares is 52. The integers are :
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Find two consecutive positive odd numbers, the sum of whose squares is 74.

Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

Mathematics

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.

Quadratic Equations

Related Questions

Two integers differ by 2 and sum of their squares is 52. The integers are :4 and 64 or 6-4 or 6-4 and -6 or 6 and 4

Find two consecutive positive odd numbers, the sum of whose squares is 74.

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Two integers differ by 2 and sum of their squares is 52. The integers are :
4 and 6
4 or 6
-4 or 6
-4 and -6 or 6 and 4